345 flanagan exam 2 5-9
TRANSCRIPT
-
7/24/2019 345 Flanagan Exam 2 5-9
1/182
Basic Concepts
Related to Kinetics Inertia
MassForce
Free body diagram
Center of Gravity
Weight
Pressure
VolumeDensity
Specific eight
!or"ue
Impulse
-
7/24/2019 345 Flanagan Exam 2 5-9
2/182
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!
http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=W0VM2i85MUMI5M&tbnid=LXb95XBLPvyfJM:&ved=0CAUQjRw&url=http%3A%2F%2Fsystematicrelativestrength.com%2F2011%2F07%2F08%2Fnever-underestimate-inertia%2F&ei=D3F3UdWrIYGR2wWKsoCwAw&bvm=bv.45580626,d.b2I&psig=AFQjCNHUk-B5R2AkwVc_hapqr7Lp-1mOag&ust=1366868606693466 -
7/24/2019 345 Flanagan Exam 2 5-9
3/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
4/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
5/182
Basic Concepts Related to Kinetics
What is weight?
attractive force that the earth exerts
on a body
t# = mag product of mass and theacceleration of gravity$ %'( m)s*"
-
7/24/2019 345 Flanagan Exam 2 5-9
6/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
7/182
Momentum
.inear
M, m v
4ngular
5 , I 6
!he moment of linearmomentum
Conservation
7st8eton9s .a
!ransfer
-
7/24/2019 345 Flanagan Exam 2 5-9
8/182
-
7/24/2019 345 Flanagan Exam 2 5-9
9/182
-
7/24/2019 345 Flanagan Exam 2 5-9
10/182
Basic Concepts Related to Kinetics
What is impulse?
the product of force and the timeover hich the force acts Ft"
units are Ns
-
7/24/2019 345 Flanagan Exam 2 5-9
11/182
Mechanical Behavior of Bodies
in ContactImpulse)
Impulse , Ft
Derived from 8eton9s Second la)
F , ma
F , m ':v;0 v7< 2 t(
Ft , 'mv;( 0 'mv7(
Ft , M
-
7/24/2019 345 Flanagan Exam 2 5-9
12/182
Mechanical Behavior of Bodies in
Contact
What is the relationship beteen impulseand momentum?
Ft = M
Ft = (mv)
! (mv)"
-
7/24/2019 345 Flanagan Exam 2 5-9
13/182
Impulse
Impulse , 'F('t(
Change in momentum
;nd8eton9s .a
'F('t( , 'm( '=V(
Force Plate
Impact
-
7/24/2019 345 Flanagan Exam 2 5-9
14/182
Mechanical Behavior of Bodies
in ContactImpact)
Perfectly elastic impact)
Perfectly plastic impact)
Coefficient of restitution)
-
7/24/2019 345 Flanagan Exam 2 5-9
15/182
Mechanical Behavior of Bodies
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;
-
7/24/2019 345 Flanagan Exam 2 5-9
16/182
-
7/24/2019 345 Flanagan Exam 2 5-9
17/182
Mechanical Behavior of Bodies in
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#
-
7/24/2019 345 Flanagan Exam 2 5-9
18/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
19/182
"e#ton$s %a#s
%a# of Inertia 4 body ill maintain a state of rest or
constant velocity unless acted on by an
e3ternal force that changes the state
-
7/24/2019 345 Flanagan Exam 2 5-9
20/182
/ s0ater has a tendency to continue gliding ithconstant speed and direction because of inertia#
"e#ton$s %a#s%a# of Inertia
-
7/24/2019 345 Flanagan Exam 2 5-9
21/182
"e#ton$s %a#s
%a# of &cceleration 4 force applied to a body causes an
acceleration of that body of a magnitude
proportional to the force% in the direction ofthe force% and inversely proportional to the
body9s mass
F , ma
-
7/24/2019 345 Flanagan Exam 2 5-9
22/182
-
7/24/2019 345 Flanagan Exam 2 5-9
23/182
-
7/24/2019 345 Flanagan Exam 2 5-9
24/182
Mechanical Behavior of Bodies
in ContactFriction)
Ma3imum static friction 'Fm()
Kinetic friction '(k):( = R
Coefficient of friction)Coefficient of static friction 's()
Coefficient of -inetic friction '-( )
8ormal reaction force)
*olling friction)
-
7/24/2019 345 Flanagan Exam 2 5-9
25/182
(riction
Static
Dynamic
1 *olling
Coefficient
*esultant
-
7/24/2019 345 Flanagan Exam 2 5-9
26/182
-
7/24/2019 345 Flanagan Exam 2 5-9
27/182
Mechanical Behavior of Bodies in
Contact
1s it easier to
pushor pulla des0
across a
room?
2ushinga des0
2ullinga des0
3 = t 4 2v
3 = t % 2v
t
t
2 2
2 2
2v
2v
25
25
-
7/24/2019 345 Flanagan Exam 2 5-9
28/182
-
7/24/2019 345 Flanagan Exam 2 5-9
29/182
"e#ton$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
-
7/24/2019 345 Flanagan Exam 2 5-9
30/182
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$s %a#s%a# of Reaction
-
7/24/2019 345 Flanagan Exam 2 5-9
31/182
"e#ton$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;(
-
7/24/2019 345 Flanagan Exam 2 5-9
32/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
33/182
Center of #ravit$
What is the center ofgravit$?
the point around hich a body-s eight
is e.ually balanced in all directionsalso referred to as the center of mass
or mass centroid
need not be physically located insideof a body"
-
7/24/2019 345 Flanagan Exam 2 5-9
34/182
Center of #ravit$
Why is the center of gravity of interest inthe study of human biomechanics?
it serves as an index of total body motion
http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=6DspVFQK-GlsDM&tbnid=fxXeRE8qbyGAWM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.xsens.com%2Fen%2Fcompany-pages%2Fcompany%2Fhuman-mocap&ei=jop3Ub_fDcnB2wWAv4GQAQ&psig=AFQjCNF65fu8QV9bCFAVK7VtHyWJRYbEBA&ust=1366875070604999 -
7/24/2019 345 Flanagan Exam 2 5-9
35/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
36/182
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>
-
7/24/2019 345 Flanagan Exam 2 5-9
37/182
%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
-
7/24/2019 345 Flanagan Exam 2 5-9
38/182
%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
-
7/24/2019 345 Flanagan Exam 2 5-9
39/182
CM
Suspension
cardinal planes
*eaction Board
Segmental Method
Stability ?
1 resist disruption Balance
1 Control e"uilibrium
-
7/24/2019 345 Flanagan Exam 2 5-9
40/182
W
SSLX
LSSXW
(7;'('
(7;'
=
=
-
7/24/2019 345 Flanagan Exam 2 5-9
41/182
-
7/24/2019 345 Flanagan Exam 2 5-9
42/182
-
7/24/2019 345 Flanagan Exam 2 5-9
43/182
-
7/24/2019 345 Flanagan Exam 2 5-9
44/182
%ta&ilit$ and Balance
What is stability?
resistance to disruption of e.uilibrium
What is balance?
ability to control e.uilibrium
-
7/24/2019 345 Flanagan Exam 2 5-9
45/182
,tailit! and Balance
Stability)
Factors that affect)
Mass% friction% center of gravity A base of
support
Balance)
Foot position affects standing balance
-
7/24/2019 345 Flanagan Exam 2 5-9
46/182
,tailit!
Mass
Friction
Sie ? base
CM ? CG lo
4nticipation
-
7/24/2019 345 Flanagan Exam 2 5-9
47/182
%ta&ilit$ and Balance
What is the base of support?area bound by the outermost regions
of contact beteen a body and
the support surface"
-
7/24/2019 345 Flanagan Exam 2 5-9
48/182
%ta&ilit$ and Balance
What can increase a body-s stability?increasing body massincreasing friction beteen the body
and the surfaces of contact
-
7/24/2019 345 Flanagan Exam 2 5-9
49/182
%ta&ilit$ and Balance
What can increase a body-s stability?increasing the size of the base of
support in the direction of an
external force
-
7/24/2019 345 Flanagan Exam 2 5-9
50/182
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
http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=neZCjdTJhzuNmM&tbnid=BpGUM5hNV_9cEM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.animatorisland.com%2Fperfect-posing-1-listen-to-the-character-and-to-physics%2F&ei=gIx3UcLOHIXr2AX5tYHwDA&psig=AFQjCNHYq2mVnKFheJKPmYohejtToIn6cw&ust=1366875599577578 -
7/24/2019 345 Flanagan Exam 2 5-9
51/182
http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=neZCjdTJhzuNmM&tbnid=BpGUM5hNV_9cEM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.animatorisland.com%2Fperfect-posing-1-listen-to-the-character-and-to-physics%2F&ei=gIx3UcLOHIXr2AX5tYHwDA&psig=AFQjCNHYq2mVnKFheJKPmYohejtToIn6cw&ust=1366875599577578 -
7/24/2019 345 Flanagan Exam 2 5-9
52/182
%ta&ilit$ and Balance
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#
-
7/24/2019 345 Flanagan Exam 2 5-9
53/182
-
7/24/2019 345 Flanagan Exam 2 5-9
54/182
"e#ton$s %a#
.inear
1 m
Inertia
4cceleration F , m a
*eaction
4ngular
1 I , m r;
1 I , m -;
Inertia 'rotating body(
! , I 'net tor"ue(
Epposite tor"ue
' l ' l f i
-
7/24/2019 345 Flanagan Exam 2 5-9
55/182
'ngular 'nalogues of inear
Kinematic uantities
What are the angular e.uivalents of linear0inematic .uantities?
9inear /ngularmass m" moment of inertia 1 = m0*"
force F" tor.ue = Fd "
momentum :=mv" angular momentum 5=m0*"
impulse Ft" angular impulse Fd t"
-
7/24/2019 345 Flanagan Exam 2 5-9
56/182
'ngular 'nalogues of *ewton+s
aws
What is the angular law of inertia?
/ rotating body ill maintain a state of
rest or constant rotational motion
unless acted on by an external
tor.ue that changes the state#
-
7/24/2019 345 Flanagan Exam 2 5-9
57/182
-
7/24/2019 345 Flanagan Exam 2 5-9
58/182
-
7/24/2019 345 Flanagan Exam 2 5-9
59/182
&ngular &nalogues of "e#ton$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>
-
7/24/2019 345 Flanagan Exam 2 5-9
60/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
61/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
62/182
,-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
-
7/24/2019 345 Flanagan Exam 2 5-9
63/182
,-uili&rium
Where do tor-ues occur within thehuman &od$?
he product of muscletension and muscle
moment arm produces a
tor.ue at the
-
7/24/2019 345 Flanagan Exam 2 5-9
64/182
,-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#
-
7/24/2019 345 Flanagan Exam 2 5-9
65/182
.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
-
7/24/2019 345 Flanagan Exam 2 5-9
66/182
%ever
.ever is a structure for transmitting energy 4 rigid bar that revolves about an a3is
or fulcrum
(ulcrum:
&
/ffort: /
Resistance: R
%ever
-
7/24/2019 345 Flanagan Exam 2 5-9
67/182
(irst Class
!he a3is 4 'or fulcrum( located beteen theeffort M and the resistance *
0&0*
R
&
/
-
7/24/2019 345 Flanagan Exam 2 5-9
68/182
,econd Class
!he resistance * is located beteen theeffort and the a3is 4 'or fulcrum(
0R04
/
&
R
i C
-
7/24/2019 345 Flanagan Exam 2 5-9
69/182
.hird Class
!he effort is located beteen theresistance * and the a3is 4 'or fulcrum(
*0/04
R
/
&
-
7/24/2019 345 Flanagan Exam 2 5-9
70/182
,-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
-
7/24/2019 345 Flanagan Exam 2 5-9
71/182
,-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#"
-
7/24/2019 345 Flanagan Exam 2 5-9
72/182
,-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
-
7/24/2019 345 Flanagan Exam 2 5-9
73/182
.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
-
7/24/2019 345 Flanagan Exam 2 5-9
74/182
%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
-
7/24/2019 345 Flanagan Exam 2 5-9
75/182
advantagemechanicalRA
EA
E
R
EA
RA
R
E
EA
RA
RE
RAREAE
==
=
=
Mechanical
-
7/24/2019 345 Flanagan Exam 2 5-9
76/182
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&
-
7/24/2019 345 Flanagan Exam 2 5-9
77/182
/&RR/
&
/1amples: ,econd Class/ &
-
7/24/2019 345 Flanagan Exam 2 5-9
78/182
/R& R/ &
/1amples: .hird Class /&
-
7/24/2019 345 Flanagan Exam 2 5-9
79/182
R/& R&
-
7/24/2019 345 Flanagan Exam 2 5-9
80/182
*
-
7/24/2019 345 Flanagan Exam 2 5-9
81/182
RS =
same
distance
same
angle
-
7/24/2019 345 Flanagan Exam 2 5-9
82/182
/1ample Racing Wheelchairs
-
7/24/2019 345 Flanagan Exam 2 5-9
83/182
-
7/24/2019 345 Flanagan Exam 2 5-9
84/182
-
7/24/2019 345 Flanagan Exam 2 5-9
85/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
86/182
d d
0
rotary
rotary
Shear)
Stabiliing
Shear)
Dislocating
-
7/24/2019 345 Flanagan Exam 2 5-9
87/182
d
d d
d
-
7/24/2019 345 Flanagan Exam 2 5-9
88/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
89/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
90/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
91/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
92/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
93/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
94/182
/-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(
-
7/24/2019 345 Flanagan Exam 2 5-9
95/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
96/182
/-uilirium
Static Dynamic
/-uations of ,tatic
-
7/24/2019 345 Flanagan Exam 2 5-9
97/182
/-uations of ,tatic
/-uilirium"uilibrium)
!hree conditions for e"uilibrium)
7> Fv, K ;> Fh, K Q> ! , K
-
7/24/2019 345 Flanagan Exam 2 5-9
98/182
/-uations of 0!namic /-uilirium
Dynamic e"uilibrium)
F30 mR3, K
Fy0 mRy, K
!G0 , K
,-uili&rium
-
7/24/2019 345 Flanagan Exam 2 5-9
99/182
,-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= ; = ;
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
100/182
Basic Concepts Related to Kinetics
*;N (;N
(m *m
67
he eights are balanced, creating e.ual
tor.ues on either side of the fulcrum#
'ngular 'nalogues of inear
-
7/24/2019 345 Flanagan Exam 2 5-9
101/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
102/182
'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
-
7/24/2019 345 Flanagan Exam 2 5-9
103/182
'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
-
7/24/2019 345 Flanagan Exam 2 5-9
104/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
105/182
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 "
-
7/24/2019 345 Flanagan Exam 2 5-9
106/182
&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
-
7/24/2019 345 Flanagan Exam 2 5-9
107/182
&ngular Momentum
Multisegmented 45ect Sum of angular momenta of individual
segments
.ocal term)*emote term)
5 , Iss mr;g
Conservation of
-
7/24/2019 345 Flanagan Exam 2 5-9
108/182
Conservation of
&ngular Momentum
!he total angular momentum of a
given system remains constant in
the absence of e3ternal tor"ues
-
7/24/2019 345 Flanagan Exam 2 5-9
109/182
.ransfer of &ngular Momentum
!ransferring angular velocity
Changing total body a3is of rotation
4symmetrical arm movements*otation of the hips 'termed hula movement(
-
7/24/2019 345 Flanagan Exam 2 5-9
110/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
111/182
-
7/24/2019 345 Flanagan Exam 2 5-9
112/182
-
7/24/2019 345 Flanagan Exam 2 5-9
113/182
-
7/24/2019 345 Flanagan Exam 2 5-9
114/182
'ngular Momentum
-
7/24/2019 345 Flanagan Exam 2 5-9
115/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
116/182
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$s
-
7/24/2019 345 Flanagan Exam 2 5-9
117/182
&ngular &nalogues of "e#ton s
%a#s of Motion8eton9s Second .a)
4 net tor"ue produces angular
acceleration of a body that is directlyproportional to the magnitude of the
tor"ue% in the same direction as the
tor"ue% and inversely proportional to
the body9s moment of inertia>
-
7/24/2019 345 Flanagan Exam 2 5-9
118/182
'ngular 'nalogues of *ewton+s
-
7/24/2019 345 Flanagan Exam 2 5-9
119/182
aws
What is the angular law ofacceleration?
/ net tor.ue causes angular acceleration
of a body that is$of a magnitude proportional to the
tor.ue
in the direction of the tor.ueand inversely proportional to the
body-s moment of inertia
'ngular 'nalogues of *ewton+s
-
7/24/2019 345 Flanagan Exam 2 5-9
120/182
g g
aws
What is the angular la of acceleration?
= 1
= m0*
-
7/24/2019 345 Flanagan Exam 2 5-9
121/182
Resistance to &ngular &cceleration
-
7/24/2019 345 Flanagan Exam 2 5-9
122/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
123/182
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*
Resistance to 'ngular 'cceleration
-
7/24/2019 345 Flanagan Exam 2 5-9
124/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
125/182
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;(
-
7/24/2019 345 Flanagan Exam 2 5-9
126/182
+uman Bod!
M f I i
-
7/24/2019 345 Flanagan Exam 2 5-9
127/182
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
Resistance to 'ngular 'cceleration
-
7/24/2019 345 Flanagan Exam 2 5-9
128/182
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@
Resistance to 'ngular 'cceleration
-
7/24/2019 345 Flanagan Exam 2 5-9
129/182
he ratio of muscular strength ability to produce tor.ue at a
-
7/24/2019 345 Flanagan Exam 2 5-9
130/182
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>
'ngular 'nalogues of *ewton+s
aws
-
7/24/2019 345 Flanagan Exam 2 5-9
131/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
132/182
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*
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
133/182
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*
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
134/182
What is stress?
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
135/182
What is volume?
space occupied by a body
has three dimensions idth, height,
and depth"
units are m@and cm@
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
136/182
What is densit$?
mass per unit of volume
represented ith the small 7ree0letter rho$
units are 0g)m@
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
137/182
What is specific weight?
eight per unit of volume
represented ith the 7ree0
letter gamma$
units are N)m@
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
138/182
! oading
What is compression?
pressing or s.ueezing force directed
axially through a body"
Ariginal
8hape 6ompression
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
139/182
What is tension?
pulling or stretching force directed
axially through a body"
Ariginal
8hape ension
! oading
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
140/182
What is shear?
force directed parallel to a surface"
Ariginal
8hape 8hear
! oading
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
141/182
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
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
142/182
What is torsion?
load producing tisting of a body
around its longitudinal axis"
Neutral
axis
! oading
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
143/182
What is deformation?
change in shape"Beformation
2lastic3egion
CltimateFailure
2oint
Dield2oint
lastic3egion
9o
ad
+asic 6oncepts 3elated to inetics
-
7/24/2019 345 Flanagan Exam 2 5-9
144/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
145/182
.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
-
7/24/2019 345 Flanagan Exam 2 5-9
146/182
Repetitive vs6 &cute %oads
*epetitive loading
4cute loading
Macrotrauma Microtrauma
Basic Concepts Related to Kinetics
-
7/24/2019 345 Flanagan Exam 2 5-9
147/182
3epetitive vs# acute loading
9i0elihood of 1n
-
7/24/2019 345 Flanagan Exam 2 5-9
148/182
,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
-
7/24/2019 345 Flanagan Exam 2 5-9
149/182
,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
-
7/24/2019 345 Flanagan Exam 2 5-9
150/182
,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
-
7/24/2019 345 Flanagan Exam 2 5-9
151/182
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 ;
-
7/24/2019 345 Flanagan Exam 2 5-9
152/182
,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 ;
-
7/24/2019 345 Flanagan Exam 2 5-9
153/182
,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 ;
-
7/24/2019 345 Flanagan Exam 2 5-9
154/182
,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
-
7/24/2019 345 Flanagan Exam 2 5-9
155/182
Kinetic uantities
lectromyography 'MG(
!o study neuromuscular function
DynamographyForces2pressure
Primarily employed in gait research
Starts% ta-eoffs% landings% baseball A golfsings% and balance
-
7/24/2019 345 Flanagan Exam 2 5-9
156/182
-
7/24/2019 345 Flanagan Exam 2 5-9
157/182
-
7/24/2019 345 Flanagan Exam 2 5-9
158/182
-
7/24/2019 345 Flanagan Exam 2 5-9
159/182
-
7/24/2019 345 Flanagan Exam 2 5-9
160/182
-
7/24/2019 345 Flanagan Exam 2 5-9
161/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
162/182
What is centripetal force?
force directed toard
the center of rotation for a
body in rotational motion"
mv* Fc= r
Fc= mr
*
Fc
Moments
-
7/24/2019 345 Flanagan Exam 2 5-9
163/182
Moments
!or"ue
Moment of force
4ngular momentum
Moment of linear
momentum
Centripetal (orce
-
7/24/2019 345 Flanagan Exam 2 5-9
164/182
Centripetal (orce
Centripetal Fc, m v; 2 r , m r 6;
Friction
Inertia
Centripetal (orce
-
7/24/2019 345 Flanagan Exam 2 5-9
165/182
Ce pe o ce
Centripetal force)
Fc, mv;2 r
Fcmr ;
Centrifugal forces are fictitious
-
7/24/2019 345 Flanagan Exam 2 5-9
166/182
Wor12 3ower2 and ,nerg$
Relationships
-
7/24/2019 345 Flanagan Exam 2 5-9
167/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
168/182
Work
Wor- , Force Distance W , Fd
Positive or-)
8egative or-) Common units) +oule '(
Mechanical or-
caloric e3penditure
Wor12 3ower2 and ,nerg$
Relationships
-
7/24/2019 345 Flanagan Exam 2 5-9
169/182
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
-
7/24/2019 345 Flanagan Exam 2 5-9
170/182
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
Wor12 3ower2 and ,nerg$
Relationships
-
7/24/2019 345 Flanagan Exam 2 5-9
171/182
What is mechanical energ$?the capacity to do or0units of energy are Eoules E"
there are three forms energy$0inetic energypotential energy
thermal energy
Work 7o#er > /nerg! Relationships/nerg!
-
7/24/2019 345 Flanagan Exam 2 5-9
172/182
/nerg!
nergy)
/nits are the same as or- 0 +oules
inetic energy '()
, 72; mv;
Potential energy 'P()
P , t h
P , magh
Strain energy 'S()
S , 72; -3;
Wor12 3ower2 and ,nerg$
Relationships
-
7/24/2019 345 Flanagan Exam 2 5-9
173/182
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"
Wor12 3ower2 and ,nerg$
Relationships
-
7/24/2019 345 Flanagan Exam 2 5-9
174/182
Buring the pole vault, the bent pole stores potential energy for
subse.uent release as 0inetic energy and thermal energy#
Conservation of Mechanical /nerg!
-
7/24/2019 345 Flanagan Exam 2 5-9
175/182
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$Relationships
5tm" 2E" Km)s" E"
-
7/24/2019 345 Flanagan Exam 2 5-9
176/182
*G
*G#H
(I
(G#J
'
;
@#(
G#G
H#G
I#@
;
G#&
'
(G#J
(I
@#;
*#H
*#;
(#H
(#;
" " " "
ime
5eight,velocity,
potential
energy, and
0inetic energychanges for a
tossed ball#
Note$
2 4 = 6
7rinciple of Work > /nerg!
-
7/24/2019 345 Flanagan Exam 2 5-9
177/182
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!
-
7/24/2019 345 Flanagan Exam 2 5-9
178/182
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!
-
7/24/2019 345 Flanagan Exam 2 5-9
179/182
M , P , constant
If Conservative forces li-e gravity
Bouncing ball 'in reality ill stop because of
friction and air resistance etc>(
-
7/24/2019 345 Flanagan Exam 2 5-9
180/182
Work
-
7/24/2019 345 Flanagan Exam 2 5-9
181/182
Changes nergy
W , F\S oule , '8m(
I$ve got the po#er
P , W 2t , F v 'Watts(
-
7/24/2019 345 Flanagan Exam 2 5-9
182/182