CONTENTS

o Angular Velocity and Accelerationo Centripetal force centrifugal force. Some illustrations of centrifugal force.o Effect on centripetal force on changing

velocity ,mass, radius.o Motion in a verticle circleo Relationship between linear and angular

accelerationo Centripetal acceleration

What is circular motion?What is circular motion?Circular motion is a motion in Circular motion is a motion in a circle at constant speed.a circle at constant speed.

Angular velocity

It is defined as the ratio of angular

displacement to the time taken by the

object to undergo the displacement.

Angular acceleration

It is defined as the ratio of change in

angular velocity of the object to the time

taken to undergo the change in angular

velocity.

Centripetal forceCentripetal forcecentrifugal forcecentrifugal force

An external force required to make a body move along circular path with uniform speed is called centripetal force.

The outward radial force experienced by an object ,when in circular motion, is called centrifugal force

• The smaller the velocity of the object, the less centripetal force you will have to apply.

Effect on centripetal force on changing velocity

Effect on centripetal force on Effect on centripetal force on changing radius.changing radius.

• The smaller the length of rope (radius ) the more centripetal force you will have to apply to the rope.

SOME ILLUSTRATIONS OF CENTRIFUGAL FORCE

CENTRIFUGE:IT IS A DEVICE USED TO SEPARATE LIGHTER PARTICLES IN SUSPENSION FROM THE MORE DENSE LIQUID IN WHICH THEY ARE CONTAINED.

Example:1)Cream is separated from the milk in cream separator.2)In sugar industries, sugar crystals are separated from the

molasses.3)The wet clothes are dried by dry cleaners in the drying machines.4)Centrifuges are used to separate honey from the wax.

MOTION IN A VERTICAL CIRCLEMOTION IN A VERTICAL CIRCLEThe motion of a mass on a string in a The motion of a mass on a string in a

verticle circle includes a number of verticle circle includes a number of mechanical concepts.mechanical concepts.

It must satisfy the constraints of It must satisfy the constraints of centripetal force to remain in a centripetal force to remain in a circle ,and must satisfy the demands circle ,and must satisfy the demands of conservation of energy as of conservation of energy as gravitational potential energy is gravitational potential energy is converted to kinetic energy when the converted to kinetic energy when the mass moves downward.mass moves downward.

MOTION IN A VERTICAL MOTION IN A VERTICAL CIRCLECIRCLE

Consider a body of mass M Consider a body of mass M tied at the end of a string and tied at the end of a string and whirled in a vertical circle of whirled in a vertical circle of radius r. let vradius r. let v1 1 and vand v22 be be velocitiesvelocities of the body and T of the body and T and T be tensions in the string and T be tensions in the string at the lowest point A and at the lowest point A and highest point B respectively.highest point B respectively.At the lowest point AAt the lowest point A

T – Mg = MvT – Mg = Mv2 2 /r/r At the highest point BAt the highest point B T + Mg = MvT + Mg = Mv22/r/r The tension T at the highest The tension T at the highest

point is zero,point is zero, 0 + Mg = Mv0 + Mg = Mv22/r/r VV2 2 = √g r= √g r

Let us find the minimum velocity the body should possess Let us find the minimum velocity the body should possess at the lowest point in order to just loop the vertical circle. at the lowest point in order to just loop the vertical circle. A/Q to the principle of conservation of energy,A/Q to the principle of conservation of energy,

K.E. of the body at point A =(P.E. +K.E.) of the body at K.E. of the body at point A =(P.E. +K.E.) of the body at point Bpoint B

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SOME ILLUSTRATIONS OF SOME ILLUSTRATIONS OF CENTRIFUGAL FORCECENTRIFUGAL FORCE

• CENTRIFUGE:IT IS A DEVICE USED TO SEPARATE LIGHTER PARTICLES IN SUSPENSION FROM THE MORE DENSE LIQUID IN WHICH THEY ARE CONTAINED.

Example:1)Cream is separated from the milk in cream separator.2)In sugar industries, sugar crystals are separated from

the molasses.3)The wet clothes are dried by dry cleaners in the drying

machines.4)Centrifuges are used to separate honey from the wax.

Centripetal accelerationCentripetal acceleration

The velocity vector at The velocity vector at any point is tangent to any point is tangent to the circular path at that the circular path at that point , the acceleration point , the acceleration vector acts along the vector acts along the radius of the circle at radius of the circle at that point and is that point and is directed towards directed towards centre.It is called the centre.It is called the centripetal acceleration.centripetal acceleration.

In this figure , the tire In this figure , the tire is spinning which is spinning which means a larger means a larger centripetal force is centripetal force is required to keep the required to keep the mud in the circular mud in the circular path of the tire.path of the tire.

In this figure ,the In this figure ,the “sticky” are adhesive “sticky” are adhesive forces from the mud forces from the mud to the tire tread are to the tire tread are large enough to be large enough to be the centripetal force the centripetal force required to keep the required to keep the mud in a circular mud in a circular path as the tire path as the tire spins.spins.

Centripetal Force CalculationCentripetal force = mass x velocity^2 / radius

Any of the data values may be changed . When finished with data entry, click on the quantity you wish to calculate in the formula above. Unit conversions will be carried out as you enter data , but values will not be forced to be consistent until you click on the desired quantity.

CALCULATION FOR:

Radius = r =

m=

m =

kg = slugs

Weight = w... N = lbs

Velocity = v= m/s = ft/s

velocity = km/h= mi\hOr in common highway speed units,

Centripetal force = F= N= lbs

Calculate Calculate

AKNOWLEDGEMENTAKNOWLEDGEMENT

I AM HIGHLY INDATETD TO OUR RESPECTED COMPUTER TEACHER, PHYSICS TEACHER FOR THEIR CONSTANT GUIDENESS TO MAKE THIS PROJECT EFFECTIVE ONE.I EXTENT MY HERTIEST THANKS TO OUR CLASSMATES FOR THEIR CO-PERATION.