1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia...
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~OPONDER
Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
~~~llilvetlie TIe velocitYastheQ~qter0fm~~11f $0 whicho9~sect -
- Q6 ItflJigidopj1ctmQveS with both traR~ili9Q ~drQtaJioQ about an axis with a fixed9QeI1taliop((or gt sectj~JQUjpgWh~l)are ther~ any P9Ints within theobjectthatalways havethe sameYelciHYii$--fue
oftn~sIt so whichones
~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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Qi9 H()theangUlarvelocitiesofthehandsofamiddotwallclockporntiotothewall0foutofthewaUAt~-jwwt
-tHampelock is unplugged do theangularaccelerationsofthe handspoint intothewalloroutefthe wan
010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
whichcase ifanydoes string wind onto the yoshyyoand in which case ifany does the string wind off the yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
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~OPONDER
Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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- Q6 ItflJigidopj1ctmQveS with both traR~ili9Q ~drQtaJioQ about an axis with a fixed9QeI1taliop((or gt sectj~JQUjpgWh~l)are ther~ any P9Ints within theobjectthatalways havethe sameYelciHYii$--fue
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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Qi9 H()theangUlarvelocitiesofthehandsofamiddotwallclockporntiotothewall0foutofthewaUAt~-jwwt
-tHampelock is unplugged do theangularaccelerationsofthe handspoint intothewalloroutefthe wan
010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
whichcase ifanydoes string wind onto the yoshyyoand in which case ifany does the string wind off the yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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Qi9 H()theangUlarvelocitiesofthehandsofamiddotwallclockporntiotothewall0foutofthewaUAt~-jwwt
-tHampelock is unplugged do theangularaccelerationsofthe handspoint intothewalloroutefthe wan
010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
whichcase ifanydoes string wind onto the yoshyyoand in which case ifany does the string wind off the yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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- Q6 ItflJigidopj1ctmQveS with both traR~ili9Q ~drQtaJioQ about an axis with a fixed9QeI1taliop((or gt sectj~JQUjpgWh~l)are ther~ any P9Ints within theobjectthatalways havethe sameYelciHYii$--fue
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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~OPONDER
Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
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Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
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Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
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Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
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Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
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Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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- Q6 ItflJigidopj1ctmQveS with both traR~ili9Q ~drQtaJioQ about an axis with a fixed9QeI1taliop((or gt sectj~JQUjpgWh~l)are ther~ any P9Ints within theobjectthatalways havethe sameYelciHYii$--fue
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
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i
Qi9 H()theangUlarvelocitiesofthehandsofamiddotwallclockporntiotothewall0foutofthewaUAt~-jwwt
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
~~~llilvetlie TIe velocitYastheQ~qter0fm~~11f $0 whicho9~sect -
- Q6 ItflJigidopj1ctmQveS with both traR~ili9Q ~drQtaJioQ about an axis with a fixed9QeI1taliop((or gt sectj~JQUjpgWh~l)are ther~ any P9Ints within theobjectthatalways havethe sameYelciHYii$--fue
oftn~sIt so whichones
~~-th~-olretion ofthe angular velocityofa rigi4objectrql~tingabo1Jt~fixe4~i~WhiU$Jhe ~a9f~etmear velocityof a particle-in arigidobjectrotatingaboutci f1Xed~P ~
~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
i
Qi9 H()theangUlarvelocitiesofthehandsofamiddotwallclockporntiotothewall0foutofthewaUAt~-jwwt
-tHampelock is unplugged do theangularaccelerationsofthe handspoint intothewalloroutefthe wan
010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
- -lt bullbull
- -imiddotT__~~ -
-~]r-Co-ae)side ofadoorTfigure) isrnade bfmafentilWitha largetirtass density- thttithe etherside Tominimize the moment of inertiaabout an axisof ni~9nalon~the~g~~h~cldili~hirtg~jpla~atth~ _--niiim_ u----- I h~Yiersideorthe lightersideExplain Heavy side Light siffe
Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
=~~~l~f~iSU~~ QIJ~
Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
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Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
Q22 Ayo-yowith halfthe string wound on its axle is placed on its edge on thefloor asshown in figureConsiderpullinggentlyon the string in the three different directions indicated by Fa Fb and Fein the figure The forcein each case is gentle enough so that the yo-yodoesnot slide In Yo-yo
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- -lt bullbull
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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~~~t~~ tyen-i7sqb~jcentctro~g aboutafixedaxishas-nonzercangulaevelocityand angularaeelerationR~q~A ~t~ ~~as Illifrom theaXiwe61ationasptgtlticlJgtBWW1iS the ratio ofthoJollowng
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
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Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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- -lt bullbull
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
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Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
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Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Ql Shouldthere be anymatterat thecenter of gravityof anobject
-- Q2 The torqueexertedbya forceabout some axis dependson thechoiceof axis Howcan thecondition
I tiext =0 be satisfiedforanychoice of axis
Q3What is the path ofa particle in a rigid object rotating about a fixed axis
Qi1lgt Wangidobjectnasoillytnli1$l~tib~ mottQu(for example the-body of a cartraveling ina ~ght lin~ on af1~troad) ~etbere~YpointswithintheobJectthat alwayshave the same velocityas thecenter 0 f mass Ifso whichones
Q5 rfaiigidobj~tbas onlyrotationalmotionabouta fixedaxis are thereanypointswitbjptb~objectthat
~~~llilvetlie TIe velocitYastheQ~qter0fm~~11f $0 whicho9~sect -
- Q6 ItflJigidopj1ctmQveS with both traR~ili9Q ~drQtaJioQ about an axis with a fixed9QeI1taliop((or gt sectj~JQUjpgWh~l)are ther~ any P9Ints within theobjectthatalways havethe sameYelciHYii$--fue
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010 Aregr ismovingforwardandslowingdOWIl Is thedirection ofteangular velocityof thewheelstoward _nO -tii~iinvee~leftot rlghtWhat is thedirection of theangularacceleration ofthe wheels -
- -lt bullbull
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Q12 C~~ider threerods made ofthesamernatedaland withthesamelengthshyag~)pass but with differentcross-sectional shapes(figure)Whicll of
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
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Q13 Is it possible to find an axis 0 f rotation (call the axis A) about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center ofmass and parallel to A
Q 14 Suppose you are designinga cart forcoastingdown a hillTomaximizeyourcoastingspeedshouldyou designthe wheels so that theirmoments of~ertia about theirrotation axes are largeor smallor does it matter Keepingthemoment ofinertiaofthe wheelsfixed wiltthe carts speedbe increasedordecreased byincreasingthe mass ofthe carts bodyAssume that mechanicalenergy isconserved
Q15 Ifaparticle is in uniformcircularmotioniseitherthedirectionorthemagnitude oftheangularmomentum aboutthecenterofits motionconstantIfthe particles speedis changingas ittrayels inacircle is either thedirectionor the magnitudeofthe angularmomentumconstant
Q16 Ifthenettorqueexerted ona particleis inthe same directionas theparticlesangularmomentumis there achange in the direction ofthe particles angularmomentumIs thereachangein the magnitudeofthe particles angularmomentum
Q 17 Consideran isolated system oftwo particlesa and b that interactwith each othersuch thatFili= -Fba hut the directionofthe forces is perpendicularto
athelinejoiningthe particles asshown in figure Whathappensto this system Fab gtas time goes on Is total linear momentum conserved Is total angular raquobull
Fba momentumconserved Is suchasystem possible Explain b
Q18Whena billiard ball rolls downa slope without sliding what force is responsible forthe torque that causestheangular acceleration about an axis through the centerofmass What force is responsible for thetorquethatcauses the angularacceleration aboutan axis throughthepointofco~~t~ththesurface
Q19 Legendhas it that a cat always lands on itsfeet High-speedcamerashave sho~ thatwhena cat begins a fallwith its feet up its tail rotates rapidlyand the eats bodyalso rotates sothatitdoes infact land on itsfeet Explainthe motion in termsofconservationofangularmomentumIncludeinyourexplanationa comparison of the sense of the rotation of the eats body with that of its tail How doyou thinka bobtailed cat might do in a fall that begins with its feet tip
Q20 Asmallsatelliteorbiting the earth hasonlyone window fortheastronautandthewindowis facing away fromtheearth Explain how the astronautcan rotate thesatelliteso he can viewthe earthand not useany rocketfuel in the process
Q21 Aspinning ice skater rapidly extends his arms [Neglect frictionduring the time interval the arms are extended] Ishis kinetic energyconserved Ishis potential energyconservedIshis mechanicalenergy conserved Is his angularmomentumconserved Ifanyofthesequantities arenotconservedtellwhether theyincrease or decrease
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![Page 58: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/58.jpg)
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![Page 59: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/59.jpg)
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![Page 60: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/60.jpg)
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![Page 61: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/61.jpg)
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![Page 62: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/62.jpg)
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![Page 63: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/63.jpg)
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![Page 67: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/67.jpg)
r3 ----_ - -shy
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![Page 68: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/68.jpg)
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PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 81: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/81.jpg)
__----+-gt V o
---- -- shy
L shy f
T
1IAJ
------___ o- v
2shy
2--shy_ yYV o
-fA ltgt~AG F (I~ 3raquo
-- --- _-
L r f
a Fe
(A00 shy
z-lvn 7 -0 ~ilJ -shy
v- ~o Y1) S
lDa-vtY Lshy
- J 70 YVfJ -=- JM M If
~
e bull - - - ---- 8ltiI Iltl-shy
c I tlt gt I
L V L
w= vT
-VL
~ w 3~ S(Vf-v~) V-r2- LCf-IZ -r V
lshy
5 Vf --+- 12shy
4
~ V~ -r-shy ~tgt
Vo cuJle l 2
- v r i- cu~ f C L-
V- r -+- r~VL ) t
tv JO~Js i1 ~ O-f Y1--~ rJilshy
i) Y - X -00 O I lt 4- VvI
Ifgt Yz7 gt_02 -_ 0-7~ y~ -z Q S - x O ~
cf
~_~-f
-fJ== Mllt-f)
-r~ s--(iO)(0176) -z lgrl
-vl(V1t QO)~))1-(Omiddotl-4-) 1J4N
P _ Yf1 ol-y _-r-r - I )
- fi ct---~--i-f--
~ 3GN
f ~ ~MJ--
--
n- W 2--1 _ r--
f =- C~ - ~~y~)v~ S ~N ~~)
~PfZ7
~ (0 J) (0)(0) ---- ---- ----_- ~--- _- _----
(lo)f)lt-) - (0(Omiddot J7cV
Sof
ogt~
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 82: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/82.jpg)
------___ o- v
2shy
2--shy_ yYV o
-fA ltgt~AG F (I~ 3raquo
-- --- _-
L r f
a Fe
(A00 shy
z-lvn 7 -0 ~ilJ -shy
v- ~o Y1) S
lDa-vtY Lshy
- J 70 YVfJ -=- JM M If
~
e bull - - - ---- 8ltiI Iltl-shy
c I tlt gt I
L V L
w= vT
-VL
~ w 3~ S(Vf-v~) V-r2- LCf-IZ -r V
lshy
5 Vf --+- 12shy
4
~ V~ -r-shy ~tgt
Vo cuJle l 2
- v r i- cu~ f C L-
V- r -+- r~VL ) t
tv JO~Js i1 ~ O-f Y1--~ rJilshy
i) Y - X -00 O I lt 4- VvI
Ifgt Yz7 gt_02 -_ 0-7~ y~ -z Q S - x O ~
cf
~_~-f
-fJ== Mllt-f)
-r~ s--(iO)(0176) -z lgrl
-vl(V1t QO)~))1-(Omiddotl-4-) 1J4N
P _ Yf1 ol-y _-r-r - I )
- fi ct---~--i-f--
~ 3GN
f ~ ~MJ--
--
n- W 2--1 _ r--
f =- C~ - ~~y~)v~ S ~N ~~)
~PfZ7
~ (0 J) (0)(0) ---- ---- ----_- ~--- _- _----
(lo)f)lt-) - (0(Omiddot J7cV
Sof
ogt~
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 83: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/83.jpg)
-fA ltgt~AG F (I~ 3raquo
-- --- _-
L r f
a Fe
(A00 shy
z-lvn 7 -0 ~ilJ -shy
v- ~o Y1) S
lDa-vtY Lshy
- J 70 YVfJ -=- JM M If
~
e bull - - - ---- 8ltiI Iltl-shy
c I tlt gt I
L V L
w= vT
-VL
~ w 3~ S(Vf-v~) V-r2- LCf-IZ -r V
lshy
5 Vf --+- 12shy
4
~ V~ -r-shy ~tgt
Vo cuJle l 2
- v r i- cu~ f C L-
V- r -+- r~VL ) t
tv JO~Js i1 ~ O-f Y1--~ rJilshy
i) Y - X -00 O I lt 4- VvI
Ifgt Yz7 gt_02 -_ 0-7~ y~ -z Q S - x O ~
cf
~_~-f
-fJ== Mllt-f)
-r~ s--(iO)(0176) -z lgrl
-vl(V1t QO)~))1-(Omiddotl-4-) 1J4N
P _ Yf1 ol-y _-r-r - I )
- fi ct---~--i-f--
~ 3GN
f ~ ~MJ--
--
n- W 2--1 _ r--
f =- C~ - ~~y~)v~ S ~N ~~)
~PfZ7
~ (0 J) (0)(0) ---- ---- ----_- ~--- _- _----
(lo)f)lt-) - (0(Omiddot J7cV
Sof
ogt~
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 84: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/84.jpg)
L r f
a Fe
(A00 shy
z-lvn 7 -0 ~ilJ -shy
v- ~o Y1) S
lDa-vtY Lshy
- J 70 YVfJ -=- JM M If
~
e bull - - - ---- 8ltiI Iltl-shy
c I tlt gt I
L V L
w= vT
-VL
~ w 3~ S(Vf-v~) V-r2- LCf-IZ -r V
lshy
5 Vf --+- 12shy
4
~ V~ -r-shy ~tgt
Vo cuJle l 2
- v r i- cu~ f C L-
V- r -+- r~VL ) t
tv JO~Js i1 ~ O-f Y1--~ rJilshy
i) Y - X -00 O I lt 4- VvI
Ifgt Yz7 gt_02 -_ 0-7~ y~ -z Q S - x O ~
cf
~_~-f
-fJ== Mllt-f)
-r~ s--(iO)(0176) -z lgrl
-vl(V1t QO)~))1-(Omiddotl-4-) 1J4N
P _ Yf1 ol-y _-r-r - I )
- fi ct---~--i-f--
~ 3GN
f ~ ~MJ--
--
n- W 2--1 _ r--
f =- C~ - ~~y~)v~ S ~N ~~)
~PfZ7
~ (0 J) (0)(0) ---- ---- ----_- ~--- _- _----
(lo)f)lt-) - (0(Omiddot J7cV
Sof
ogt~
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 85: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/85.jpg)
e bull - - - ---- 8ltiI Iltl-shy
c I tlt gt I
L V L
w= vT
-VL
~ w 3~ S(Vf-v~) V-r2- LCf-IZ -r V
lshy
5 Vf --+- 12shy
4
~ V~ -r-shy ~tgt
Vo cuJle l 2
- v r i- cu~ f C L-
V- r -+- r~VL ) t
tv JO~Js i1 ~ O-f Y1--~ rJilshy
i) Y - X -00 O I lt 4- VvI
Ifgt Yz7 gt_02 -_ 0-7~ y~ -z Q S - x O ~
cf
~_~-f
-fJ== Mllt-f)
-r~ s--(iO)(0176) -z lgrl
-vl(V1t QO)~))1-(Omiddotl-4-) 1J4N
P _ Yf1 ol-y _-r-r - I )
- fi ct---~--i-f--
~ 3GN
f ~ ~MJ--
--
n- W 2--1 _ r--
f =- C~ - ~~y~)v~ S ~N ~~)
~PfZ7
~ (0 J) (0)(0) ---- ---- ----_- ~--- _- _----
(lo)f)lt-) - (0(Omiddot J7cV
Sof
ogt~
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 86: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/86.jpg)
tv JO~Js i1 ~ O-f Y1--~ rJilshy
i) Y - X -00 O I lt 4- VvI
Ifgt Yz7 gt_02 -_ 0-7~ y~ -z Q S - x O ~
cf
~_~-f
-fJ== Mllt-f)
-r~ s--(iO)(0176) -z lgrl
-vl(V1t QO)~))1-(Omiddotl-4-) 1J4N
P _ Yf1 ol-y _-r-r - I )
- fi ct---~--i-f--
~ 3GN
f ~ ~MJ--
--
n- W 2--1 _ r--
f =- C~ - ~~y~)v~ S ~N ~~)
~PfZ7
~ (0 J) (0)(0) ---- ---- ----_- ~--- _- _----
(lo)f)lt-) - (0(Omiddot J7cV
Sof
ogt~
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
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--
n- W 2--1 _ r--
f =- C~ - ~~y~)v~ S ~N ~~)
~PfZ7
~ (0 J) (0)(0) ---- ---- ----_- ~--- _- _----
(lo)f)lt-) - (0(Omiddot J7cV
Sof
ogt~
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 88: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/88.jpg)
(fo ) oJ)x =Cr)(~f(0- -gt0
ox- -J-J~
-------------------- ----------------_ -__-_--- -------shy-----_M _
v(b) yen-r =- CAJ () e) z cA v
---------lshy VL-- z w (R-h) -z vrLshy- - --- ~ - - - - -
~ z w(o) -z 0
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 89: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/89.jpg)
v -==- ccraquo )6lt d(
f
~) VAjgtVgtvvc -- 0 If c (X c p
- 0 YVp-- f
C gt
~Lv~ -r~JR F 2shy(
~middot4 I~r
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 90: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/90.jpg)
~ frrftn ~ c lxuA~ oY
fr~_~~h~~
is I_--rshy
--___ _------ shy_c---~middotmiddot~middot~middot-middot--middot-middotmiddot~~--------middot- -shyf~middot - --- - ______ _2Z~~ --- - --shy
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 91: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/91.jpg)
---
--------__----------------~--~ -----~---- - shy
l middot
J2shyP ~gt-5)
IN ~tJ
w ~ ~Omiddot- (ltt)t ~ ~- ~~~)~ f
jYI~ v~WY
(1J) t =- fO ~ (~~~) ~
0D l == W(Ilt - IJRLe-shy klt--)
t-- tuo K - --
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 92: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/92.jpg)
fit ~
r~ ~ ~ ~ 01~
rt J-lt~ ~ tze ~ ~ - r~~
AY~ b~ ~(~ ~
7~~h +~
2-e ~~~ ~ ze
~~~~
~~~~-~
~~~A~~~
Pvi~ ~ I~ ~
01t~)c __ ~ ~ v 1 )+ E1 k2)w
0Kj vJo = M(poundL-tK]W
---0--~W -= - W6K LR L-- ~ L 0
--- L
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 93: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/93.jpg)
2-shyW
o
I ~ -]I k i
I e-t JeL-I
-------shy
t7)
J(2- -shy-(
-
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 94: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/94.jpg)
~7 ~---------_
~-
oZ
1-1( l laquo-fJ ( -S
1
--6L )_---S==-~=----------c --=
C) r- f- - rJ 0shy
9 F( -t- F -= I(~)
jUA
I 1R
bull I
PiC- -f- P-f =- ~ C- - tv10( f( ~
~ =- (T2- -~)Q
V~ 5- hCA-lt2-- cAgt--rdJgt-1-t
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 95: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/95.jpg)
4) j1 -ampl
l--~e~J 1
c-5shy wI 1fshy r~ ~
==-0~
_-- --- -- ----- - ---_---- __--_
- - - --
f
middot --- ---~-
gtgt --
![Page 96: 1 - PACE IIT & Medical Best coaching classes for IIT, JEE ... · about which the moment of inertia for an object is smaller than the moment of inertia about an axis through the center](https://reader036.fdocuments.in/reader036/viewer/2022062916/5ecc1077ed65ea4eb03407a0/html5/thumbnails/96.jpg)
middot --- ---~-
gtgt --