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Basic Concepts

Related to Kinetics Inertia

MassForce

Free body diagram

Center of Gravity

Weight

Pressure

VolumeDensity

Specific eight

!or"ue

Impulse

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Basic Concepts Related to Kinetics

What is inertia?

resistance to change in state of motion

proportional to mass

at rest it is mass

gravity acts in y axis only

has no units!
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Inertia

inertia #the tendency of a body to resist a change in its state of

motion$ no units% but directly proportional to mass &

Mass 'm( ) *esist a change in its state of linear motion

the "uantity of matter contained in an ob+ect$ units , -g 'lb(

mass moment of inertia 'I() *esist a change in its stateof angular motion

I = m r2 units: kg m2

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What is force?

a push or a pull

characterized by magnitude,

direction, and point of application

F = maunit is the Neton N"

Basic Concepts

Related to Kinetics

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What is weight?

attractive force that the earth exerts

on a body

t# = mag product of mass and theacceleration of gravity$ %'( m)s*"

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Mechanical Behavior of Bodies

in Contact.inear Momentum)

M , mv

/nits 0 -g 1 m2s

Principle of conservation of momentum)

In the absence of e3ternal forces% the totalmomentum of a given system remainsconstant

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Momentum

.inear

M, m v

4ngular

5 , I 6

!he moment of linearmomentum

Conservation

7st8eton9s .a

!ransfer

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What is impulse?

the product of force and the timeover hich the force acts Ft"

units are Ns

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in ContactImpulse)

Impulse , Ft

Derived from 8eton9s Second la)

F , ma

F , m ':v;0 v7< 2 t(

Ft , 'mv;( 0 'mv7(

Ft , M

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Mechanical Behavior of Bodies in

Contact

What is the relationship beteen impulseand momentum?

Ft = M

Ft = (mv)

! (mv)"

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Impulse

Impulse , 'F('t(

Change in momentum

;nd8eton9s .a

'F('t( , 'm( '=V(

Force Plate

Impact

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in ContactImpact)

Perfectly elastic impact)

Perfectly plastic impact)

Coefficient of restitution)

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in ContactImpact 'cont>( ? Coefficient of *estitution

8eton)

When to bodies undergo a direct collision% thedifference in their velocities immediately afterimpact is proportional to the difference in theirvelocities immediately before impact

0e , relative velocity after impact , v70 v;

relative velocity before impact u70 u;

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Contact

+all velocities before impact

+all velocities after impact

u( u*

v( v*

v(% v*= %e u(% u*"

he differences in

to balls- velocities

before impact is

proportional to the

difference in their

velocities after

impact# he factor of

proportionality is the

coefficient ofrestitution#

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What is a free od! diagram@

'diagram shoing vector representations of all

forces acting on a defined system(

ball eight

Force appliedby rac.uet

/ir resistance

+all being

struc0 by a

rac.uet

Basic Concepts

Related to Kinetics

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"e#ton$s %a#s

%a# of Inertia 4 body ill maintain a state of rest or

constant velocity unless acted on by an

e3ternal force that changes the state

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/ s0ater has a tendency to continue gliding ithconstant speed and direction because of inertia#

"e#ton$s %a#s%a# of Inertia

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"e#ton$s %a#s

%a# of &cceleration 4 force applied to a body causes an

acceleration of that body of a magnitude

proportional to the force% in the direction ofthe force% and inversely proportional to the

body9s mass

F , ma

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in ContactFriction)

Ma3imum static friction 'Fm()

Kinetic friction '(k):( = R

Coefficient of friction)Coefficient of static friction 's()

Coefficient of -inetic friction '-( )

8ormal reaction force)

*olling friction)

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(riction

Static

Dynamic

1 *olling

Coefficient

*esultant

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Contact

1s it easier to

pushor pulla des0

across a

room?

2ushinga des0

2ullinga des0

3 = t 4 2v

3 = t % 2v

t

t

2 2

2 2

2v

2v

25

25

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"e#ton$s %a#s

%a# of Reaction For every action% there is an e"ual and

opposite reaction

When one body e3erts a force on a second%

the second body e3erts a reaction for that is

e"ual in magnitude and opposite indirection of the first body

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t

3

1n accordance ith the

la of reaction, the eight

of a box sitting on a table

generates a reactionforceby the table that is e.ual

in magnitude and

opposite in direction to the

eight#

"e#ton$s %a#s%a# of Reaction

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"e#ton$s %a#s

%a# of *ravitation 4ll bodies are attracted to one another ith

a force proportional to the product of the

masses and inversely proportional to thes"uare of the distance beteen them

Fg, G'm7m;2 d;(

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What is the center of gravit!@

1point around hich a body9s eight ise"ually balanced in all directions1point that serves as an inde3 of total body

motion1point at hich the eight vector acts1same as the center of mass

Basic Concepts

Related to Kinetics

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Center of #ravit$

What is the center ofgravit$?

the point around hich a body-s eight

is e.ually balanced in all directionsalso referred to as the center of mass

or mass centroid

need not be physically located insideof a body"

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Center of #ravit$

Why is the center of gravity of interest inthe study of human biomechanics?

it serves as an index of total body motion
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Center of #ravit$

Why is the center of gravity of interest inthe study of human biomechanics?

the body responds to external forces

as though all mass ereconcentrated at the 67

this is conse.uently the point at hich

the eight vector is shon to act ina free body diagram

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Center of *ravit! 'C*)

Center of MassCenter of Mass 2 Center of Gravity)

!he CG of a symmetrical ob+ect of

homogeneous density% is the e3act center ofthe ob+ect

When mass distribution is not constant% CG

shifts in the direction of greater mass>

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%ocating the Center of *ravit!

For one0segment% balance point in three

different planes

4s pro+ectile% the body9s CG follos aparabolic tra+ectory

Weight vector acts as the CG

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%ocating the +uman Bod!

Center of *ravit!*eaction board)

re"uires a scale% a platform A rigid board

ith sharp supports on either end>

Segmental method)

uses data for average locations of individual

body segments CGs as related to a

percentage of segment length

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CM

Suspension

cardinal planes

*eaction Board

Segmental Method

Stability ?

1 resist disruption Balance

1 Control e"uilibrium

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W

SSLX

LSSXW

(7;'('

(7;'

=

=

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%ta&ilit$ and Balance

What is stability?

resistance to disruption of e.uilibrium

What is balance?

ability to control e.uilibrium

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,tailit! and Balance

Stability)

Factors that affect)

Mass% friction% center of gravity A base of

support

Balance)

Foot position affects standing balance

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,tailit!

Mass

Friction

Sie ? base

CM ? CG lo

4nticipation

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What is the base of support?area bound by the outermost regions

of contact beteen a body and

the support surface"

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What can increase a body-s stability?increasing body massincreasing friction beteen the body

and the surfaces of contact

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What can increase a body-s stability?increasing the size of the base of

support in the direction of an

external force

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8tability and +alance

What can increase a body-s stability?horizontally positioning the center of

gravity near the edge of the base of

support on the side of the external forc
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What can increase a body-s stability?vertically positioning the center of

gravity as lo as possible

d

d d

he higher the

67, the greater

the amount of

tor.ue its motion

creates about

the supportsurface#

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"e#ton$s %a#

.inear

1 m

Inertia

4cceleration F , m a

*eaction

4ngular

1 I , m r;

1 I , m -;

Inertia 'rotating body(

! , I 'net tor"ue(

Epposite tor"ue

' l ' l f i

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'ngular 'nalogues of inear

Kinematic uantities

What are the angular e.uivalents of linear0inematic .uantities?

9inear /ngularmass m" moment of inertia 1 = m0*"

force F" tor.ue = Fd "

momentum :=mv" angular momentum 5=m0*"

impulse Ft" angular impulse Fd t"

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'ngular 'nalogues of *ewton+s

aws

What is the angular law of inertia?

/ rotating body ill maintain a state of

rest or constant rotational motion

unless acted on by an external

tor.ue that changes the state#

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&ngular &nalogues of "e#ton$s

%a#s of Motion8eton9s First .a)

4 rotating body ill maintain a state of

constant rotational motion unless acted

on by an e3ternal tor"ue>

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What is a tor-ue '.)?

1the rotary effect of a force

1the angular e"uivalent of force

1also -non as moment of force% the product

of force and the force9s moment arm 'the

shortest perpendicular distance beteen a

force9s line of action and an a3is of rotation(

Basic Concepts

Related to Kinetics

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What is a tor-ue@

! , Fd 'the product of force and the

perpendicular distance from the force9s line

of action to the a3is of rotation(

axis

d = *mF = (;N

Basic ConceptsRelated to Kinetics

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,-uili&rium

.he moment arm

of a force is the

perpendicular

distance from theforce+s line of

action to the a/is

of rotation0

:oment armForce

line of

action

:oment

arm

Force

line of

action

axis

axis

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,-uili&rium

Where do tor-ues occur within thehuman &od$?

he product of muscletension and muscle

moment arm produces a

tor.ue at the

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,-uili&rium

80illed pitchers often maximize the length of the moment armbeteen the hand and total%body axis of rotation during the

delivery of a pitch to maximize the effect of the tor.ue

produced by the muscles#

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.uilibrium

What is a lever?

a simple machine consisting of a

relatively rigid bar%li0e body that

can be made to rotate about anaxis or a fulcrum

there are first, second, and third

class levers

%ever

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%ever

.ever is a structure for transmitting energy 4 rigid bar that revolves about an a3is

or fulcrum

(ulcrum:

&

/ffort: /

Resistance: R

%ever

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(irst Class

!he a3is 4 'or fulcrum( located beteen theeffort M and the resistance *

0&0*

R

&

/

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,econd Class

!he resistance * is located beteen theeffort and the a3is 4 'or fulcrum(

0R04

/

&

R

i C

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.hird Class

!he effort is located beteen theresistance * and the a3is 4 'or fulcrum(

*0/04

R

/

&

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,-uili&rium

3elative locations

of the applied

force F", the

resistance 3",and the fulcrum

or axis of rotation

determine lever

classifications#

F 3

First class

3 F

8econd class

F 3

hird class

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,-uili&rium

What is mechanicaladvantage? he ratio of the moment arm of the

force force arm" to the moment

arm of the resistance resistance

arm" for a given lever When the ratio is greater than (,

the re.uired force is less thanresistive force force m#a#>res#

m#a#"

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,-uili&rium

' force can &alance a larger

resistance when the force arm islonger than the resistance arm0

F = (;N 3 = *;N

Fa=*m 3a=(m

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.uilibrium

' force can move a resistance through alarge range of motion when the force arm(Fa) is shorter than the resistance arm (Ra)0

F 3Fa

3a

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%ever ,!stems

Moment arm of applied force moment arm of

resistance

*esistance arm is longer than force arm

Mechanical advantage , Moment arm 'force(

Moment arm 'resistance(

RAREAE

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advantagemechanicalRA

EA

E

R

EA

RA

R

E

EA

RA

RE

RAREAE

==

=

=

Mechanical

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Mechanical

&dvantage or 0isadvantage

Second Class

First Class

hen 4 *4

ffort H *esistance

!hird Class

First Class

hen *4 4

ffort *esistance

/1amples: (irst Class&

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/&RR/

&

/1amples: ,econd Class/ &

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/R& R/ &

/1amples: .hird Class /&

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R/& R&

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*

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RS =

same

distance

same

angle

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/1ample Racing Wheelchairs

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&natomical %evers

In the human body% most lever systems are thirdclass

4rrangement promotes*ange of motion

4ngular speed

Forces generated must be in e3cess of the

resistance force !o components of muscular force

rotary and parallel component

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d d

0

rotary

rotary

Shear)

Stabiliing

Shear)

Dislocating

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d

d d

d

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&ngle of pull 4ngle beteen the line of pull of the muscle A the

bone on hich it inserts 'angle of attachment

facing aay from +oint as opposed to angle on side

of +oint(

With every degree of +oint motion% the angle ofpull changes

oint movements A insertion angles involve

mostly small angles of pull

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&ngle of pull 4ngle of pull decreases as bone moves aay

from its anatomical position through localmuscle group9s contraction

*ange of movement depends on type of +ointA bony structure

Most muscles or- at angles of pull lessthan JK degrees

4mount of muscular force needed to cause+oint movement is affected by angle of pull

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&ngle of pullRotary component (vertical component( 0

component of muscular force that acts

perpendicular to long a3is of bone 'lever(

When the line of muscular force is at LK degrees

to bone on hich it attaches% all of the muscularforce is rotary force '7KK of force is

contributing to movement(

4ll of force is being used to rotate the lever about

its a3is

!he closer the angle of pull to LK degrees% the

greater the rotary component

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&ngle of pull

4t all other degrees of the angle of pull% oneof the other to components of force are

operating in addition to rotary component

*otary component continues ith less force% to

rotate the lever about its a3is

Second force component is the horiontal% or

nonrotary componentand is either astabilizing

componentor a dislocating component%depending on hether the angle of pull is less

than or greater than LK degrees

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&ngle of pull If angle is less than LK

degrees% the force is astabilizingforce because itspull directs the bone toardthe +oint a3is

If angle is greater than LKdegrees% the force is

dislocatingdue to its pulldirecting the bone aay fromthe +oint a3is

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&ngle of pull

Sometimes desirable to begin ith the angle

of pull is at LK degrees

chin0up 'pull0up(angle ma-es the chin0up easier because of

more advantageous angle of pull

compensate for lac- of sufficient strength

/ ili i

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/-uilirium

.or-ue!or"ue)

! , Fd

Moment arm) In the body% moment arm of muscle is the

perpendicular distance beteen muscleNs line pulland +oint center

.argest moment arm at an angle of pull OLKK Vector "uantity% magnitude and direction

FdA countercloc-ise '( A cloc-ise '0(

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Resultant 3oint .or-ues

Product of muscle tension and muscle moment armproduces a tor"ue at the +oint crossed by themuscle

4gonist and antagonist muscle groups 8et +oint tor"ue

Concentric and eccentric

!o +oint muscles Factors that affect net +oint tor"ues

Speed9s affect on net +oint tor"ues

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/-uilirium

Static Dynamic

/-uations of ,tatic

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/-uations of ,tatic

/-uilirium"uilibrium)

!hree conditions for e"uilibrium)

7> Fv, K ;> Fh, K Q> ! , K

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/-uations of 0!namic /-uilirium

Dynamic e"uilibrium)

F30 mR3, K

Fy0 mRy, K

!G0 , K

,-uili&rium

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,-uili&rium

What is statice-uili&rium?a motionless state in hich there is no

net force or net tor.ue acting

the conditions of static e.uilibrium are$

Fv= ;

Fh= ; = ;


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*;N (;N

(m *m

67

he eights are balanced, creating e.ual

tor.ues on either side of the fulcrum#

'ngular 'nalogues of inear

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Kinematic uantities

What are the angular e.uivalents of linear0inematic .uantities?

9inear /ngularmass m" moment of inertia 1 = m0*"

force F" tor.ue = Fd "

momentum :=mv" angular momentum 5=m0*"

impulse Ft" angular impulse Fd t"

'ngular Momentum

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'ngular Momentum

What is angular momentum?.uantity of angular motion possessed

by a body

measured as the product of moment of

inertia and angular velocity$

5 = 1

5 = m0*

'ngular Momentum

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'ngular Momentum

/ngular momentum is the sum of the localterm 1ss" and the remote term mr*g"#

5 = 1ss4 mr*g

C#

C#s

s

g

'ngular Momentum

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gu a o e tu

What is the principle of conservationof angular momentum?

he total angular momentum of a given

system remains constant in theabsence of external tor.ues#

5(

= 5*

m0*"(= m0*"*

'ngular Momentum

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g

When angular momentum is conserved, there is a

tradeoff beteen moment of inertia and angular

velocity#

uc0 position = small 1, large "

xtended position = large 1, small "

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&ngular Momentum

4ngular momentum)

For linear motion) M , mv

For angular motion) 5 , IC Er) 5 ? m- ;

Factors that affect a angular momentum

Mass 'm(% distribution of mass ith respect tothe a3is or rotation '-( % angular velocity of the

body '(

&ngular Momentum

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&ngular Momentum

Multisegmented 45ect Sum of angular momenta of individual

segments

.ocal term)*emote term)

5 , Iss mr;g

Conservation of

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Conservation of

&ngular Momentum

!he total angular momentum of a

given system remains constant in

the absence of e3ternal tor"ues

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.ransfer of &ngular Momentum

!ransferring angular velocity

Changing total body a3is of rotation

4symmetrical arm movements*otation of the hips 'termed hula movement(

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Change in &ngular Momentum

Depend on only on the magnitude and

direction% but also on the length of time

.inear impulse , Ft4ngular impulse !t

Impulse0momentum relationship)

!t , 5!t , 'I(;0 'I(7

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'ngular Momentum

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What produces change in angular

momentum?

angular impulse % the product of tor.ue

and the time interval over hich the

tor.ue acts$

t = 5

t = 1"*% 1"(

'ngular Momentum

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8pringboard reaction force F" multiplied by its moment arm

from the diver-s 67 d " creates a tor.ue that generates the

angular impulse that produces angular momentum at ta0eoff# t = 5

C#d

F

+ac0ard

somersault

&ngular &nalogues of "e#ton$s

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&ngular &nalogues of "e#ton s

%a#s of Motion8eton9s Second .a)

4 net tor"ue produces angular

acceleration of a body that is directlyproportional to the magnitude of the

tor"ue% in the same direction as the

tor"ue% and inversely proportional to

the body9s moment of inertia>

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aws

What is the angular law ofacceleration?

/ net tor.ue causes angular acceleration

of a body that is$of a magnitude proportional to the

tor.ue

in the direction of the tor.ueand inversely proportional to the

body-s moment of inertia


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g g

aws

What is the angular la of acceleration?

= 1

= m0*

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Resistance to &ngular &cceleration

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Resistance to &ngular &ccelerationMoment of Inertia

*esistance to linear accelerationMass

*esistance to angular accelerationMass

Distribution of mass ith respect to a3is ofrotation

I , mr;

I , mr;

Resistance to 'ngular 'cceleration

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r rr

rm mm

m

axis of rotation

:oment of inertia is the sum of the

products of each particle-s mass m"

and the radius of rotation r" for thatparticle s.uared# 1 = mr*


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What is the radius of g$ration?distance from the axis of rotation to a

point here the body-s mass could

be concentrated ithout altering its

rotational characteristics

used as the index for mass distribution

for calculating moment ofinertia$

1 = m0*

0 t i i M t f I ti

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0etermining Moment of Inertia

I , m-;

*adius of gyration)

8ot the same as the segmental CG

.ength changes as the a3is of rotation changes

/nits of moment of inertia consist of mass

multiplied by units of length s"uared ' -g1m;(

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+uman Bod!

M f I i

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Moment of Inertia In sagittal and frontal plane motion

43is passing through center of pro3imal +oint

5uman body as a hole

*otates free of support% around 7 of Q principle a3es!ransverse 'frontal(

4nteroposterior 'sagittal(

.ongitudinal 'vertical(

Principal moment of inertia


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nee angle affects the moment of inertia of the

singing leg ith respect to the hip because ofchanges in the radius of gyration for the loer leg

0*" and foot 0@"#

0(

0*0@

0(

0*0@


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he ratio of muscular strength ability to produce tor.ue at a

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g g

%a#s of Motion

8eton9s !hird .a)

For every tor"ue e3erted by one body

on another% there is an e"ual andopposite tor"ue e3erted by the second

body on the first>


aws

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aws

What is the angular law of reaction?

For every angular action, there is an

e.ual and opposite angular reaction#When one body exerts a tor.ue on a

second, the second body exerts a

reaction tor.ue that is e.ual inmagnitude and opposite in direction

on the first body#

Basic Concepts Related

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to Kinetics

What is pressure?

force per unit of area over hich theforce acts

commonly used to describe force

distribution ithin a fluid e#g#blood pressure, ater pressure"

units are N)m*


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What is stress?

force per unit of area over hich

the force acts

commonly used to describe force

distribution ithin a solid

units are N)m*


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What is stress?


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What is volume?

space occupied by a body

has three dimensions idth, height,

and depth"

units are m@and cm@


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What is densit$?

mass per unit of volume

represented ith the small 7ree0letter rho$

units are 0g)m@


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What is specific weight?

eight per unit of volume

represented ith the 7ree0

letter gamma$

units are N)m@


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! oading

What is compression?

pressing or s.ueezing force directed

axially through a body"

Ariginal

8hape 6ompression


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What is tension?

pulling or stretching force directed

axially through a body"

Ariginal

8hape ension

! oading


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What is shear?

force directed parallel to a surface"

Ariginal

8hape 8hear

! oading


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What is &ending?

asymmetric loading that produces tension

on one side of a body-s longitudinal axis

and compression on the other side"

6ompression

ension

! oading


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What is torsion?

load producing tisting of a body

around its longitudinal axis"

Neutral

axis

! oading


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What is deformation?

change in shape"Beformation

2lastic3egion

CltimateFailure

2oint

Dield2oint

lastic3egion

9o

ad

+asic 6oncepts 3elated to inetics

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What are repetitiveand acuteloading?repetitive$ repeated application of a

subacute load that is usually of

relatively lo magnitude

acute$ application of a single force of

sufficient magnitude to cause

in

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.he /ffects of %oading

Deformation

When an e3ternal force is applied to the human

body% several factors influence hether an in+ury

occurs

Magnitude and direction of force

4rea over hich force is distributed

.oad0deformation curve

Tield point 'elastic limit(

Failure

Repetitive vs &cute %oads

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Repetitive vs6 &cute %oads

*epetitive loading

4cute loading

Macrotrauma Microtrauma


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3epetitive vs# acute loading

9i0elihood of 1n

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,ample 7rolem 8

7> If a scale shos that an individual has amass of U -g% hat is that individual9seight@

non) m , U -g

Solution 4nser

Wanted) eight t , UUX 8

Formulas) t , mag t , 7JK lbs

7 -g , ;>; lbs

,ample 7rolem 8

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,ample 7rolem 8

;> What is the mass of an ob+ect eighting

7;KK 8@

non) t , 7;KK 8Solution 4nser

Wanted) mass m , 7;;>Q; -g

Formulas) t , mag

,ample 7rolem 2

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,ample 7rolem 2

Is it better to be stepped on by a omen earing a spi-e or by acourt shoe@

non) t , JJU 8 4s, Y cm; 4c, 7XJ cm;

SolutionWanted) 4nser

Pressure e3erted by the spi-e heel p , 7QL82cm;

Pressure e3erted by the court shoe p , Q> 82Cm;

Formulas) p , F24 YQ>XJ times more pressure

Common 9nits for

Kinetic uantities

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Kinetic uantities

Zuantity Symbol Metric /nit nglish /nitMass m -g slug

Force F 8 lb

Pressure P Pa psi

Volume 'solids( V mQ ftQ

'li"uids( liter gallon

Density -g2mQ lb2ftQ

Specific eight 82mQ lb2ftQ

!or"ue ! 80m ft0lb

Impulse 8 1 s lb 1 s

,ample 7rolem ;

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,ample 7rolem ;

5o much compressive stress is

present on the .7% .; vertebral dis- of

a U;J 8 oman% given thatappro3imately YJ of body eight is

supported by the dis-

,ample 7rolem ;

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,ample 7rolem ;

a( When she stands in anatomical positions@

Given) F , 'U;J 8( 'K>YJ( 4 , ;K cm;

Formula) Stress , F24

Stress , 'U;J 8( 'K>YJ( 2 ;K cm;

Stress , 7Y 8 2 cm;

,ample 7rolem ;

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,ample 7rolem ;

b( When she stands erect holding a ;;; 8suitcase@

Given) F , 'U;J 8( 'K>YJ( , ;;; 8 4 , ;Kcm;

Formula) Stress , F24

Stress , 'U;J 8( 'K>YJ( ;;; 8 2 ;K cm;

Stress , ;J>; 8 2 cm;

.ools for Measuring

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Kinetic uantities

lectromyography 'MG(

!o study neuromuscular function

DynamographyForces2pressure

Primarily employed in gait research

Starts% ta-eoffs% landings% baseball A golfsings% and balance

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vector

physical "uantity that possesses both magnitude and direction scalar

physical "uantity that is completely described by its magnitude

vector compositionprocess of determining a single vector from to or more

vectors by vector addition

vector resolutionoperation that replaces a single vector ith to perpenticular

vectors such that the vector composition of the toperpendicular vectors yields the original vector

Centripetal Force

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What is centripetal force?

force directed toard

the center of rotation for a

body in rotational motion"

mv* Fc= r

Fc= mr

*

Fc

Moments

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Moments

!or"ue

Moment of force

4ngular momentum

Moment of linear

momentum

Centripetal (orce

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Centripetal (orce

Centripetal Fc, m v; 2 r , m r 6;

Friction

Inertia

Centripetal (orce

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Ce pe o ce

Centripetal force)

Fc, mv;2 r

Fcmr ;

Centrifugal forces are fictitious

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Wor12 3ower2 and ,nerg$

Relationships

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What is mechanical wor1?

the product of a force applied against a

resistance and the displacement of

the resistance in the direction of the forceW = Fd

units of or0 are Eoules E"

Work 7o#er > /nerg! RelationshipsW k

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Work

Wor- , Force Distance W , Fd

Positive or-)

8egative or-) Common units) +oule '(

Mechanical or-

caloric e3penditure


Relationships

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p

What is mechanical power?the rate of or0 productioncalculated as or0 divided by the time

over hich the or0 as done W

2 = t

units of or0 are Watts W"

Work 7o#er > /nerg! Relationships7

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7o#er

Poer , Wor- , W

change in time t

Poer , force 3 distance , Fd change in time t

Since v , d 2 t% Poer , Fv

/nits 0 atts 'W( 7 W , 7 2s


Relationships

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What is mechanical energ$?the capacity to do or0units of energy are Eoules E"

there are three forms energy$0inetic energypotential energy

thermal energy

Work 7o#er > /nerg! Relationships/nerg!

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/nerg!

nergy)

/nits are the same as or- 0 +oules

inetic energy '()

, 72; mv;

Potential energy 'P()

P , t h

P , magh

Strain energy 'S()

S , 72; -3;


Relationships

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What is 1inetic energ$?energy of motion

= mv*

What is potential energ$?energy by virtue of a body-s position or

configuration

2 = t"ht"


Relationships

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Buring the pole vault, the bent pole stores potential energy for

subse.uent release as 0inetic energy and thermal energy#

Conservation of Mechanical /nerg!

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g!

Consider a ball tossed vertically into the air

.a of conservation of mechanical energy)

When gravity is the only acting e3ternalforce% a body9s mechanical energy remain

constant

'P ( , C

Wor12 3ower2 and ,nerg$Relationships

5tm" 2E" Km)s" E"

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*G

*G#H

(I

(G#J

'

;

@#(

G#G

H#G

I#@

;

G#&

'

(G#J

(I

@#;

*#H

*#;

(#H

(#;

" " " "

ime

5eight,velocity,

potential

energy, and

0inetic energychanges for a

tossed ball#

Note$

2 4 = 6

7rinciple of Work > /nerg!

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p g!

!he or- of a force is e"ual to the changein energy that it produces on the ob+ectacted on

W , P ! 'here ! isthermal energy(

Mechanical or- caloric e3penditure

O;J of energy consumed by muscle isconverted into or-

/nerg!

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g!

Potential

P, 'mg( h

7osition dependent

Strain

S,72; - 3;

inetic

velocit! dependent

.inear

,72; m v;

4ngulara,72; I 6;

Conservation of /nerg!

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M , P , constant

If Conservative forces li-e gravity

Bouncing ball 'in reality ill stop because of

friction and air resistance etc>(

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Work

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Changes nergy

W , F\S oule , '8m(

I$ve got the po#er

P , W 2t , F v 'Watts(

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345 Flanagan Exam 2 5-9

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