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Chapter 11:
The Description of
Human Motion
KINESIOLOGY
Scientific Basis of Human Motion, 11th edition
Hamilton, Weimar & Luttgens
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
© 2008 McGraw-Hill Higher Education. All Rights Reserved.
Objectives
1. Name the motions experienced by the human body,
and describe the factors that cause & modify motion.
2. Name & properly use terms that describe linear &
rotary motion.
3. Explain the interrelationship that exist among
displacement, velocity, & acceleration, & use them to
describe & analyze human motion.
4. Describe behavior of projectiles, & explain how angle,
speed, & height of projection affect that behavior.
5. Describe relationship between linear & rotary
movement, & explain significance to human motion.
6. Identify kinematic components used to describe
skillful performance of a motor task .
© 2008 McGraw-Hill Higher Education. All Rights Reserved.
Relative Motion
• Motion is the act or process of changing
place or position with respect to some
reference object.
• At rest or in motion depends totally on the
reference.
• Sleeping passenger in a flying plane:
– At rest in reference to the plane.
– In motion in reference to the earth.
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Cause of Motion
• The cause of motion is a form of force.
• Force is the instigator of movement.
• Force must be sufficiently great to overcome
the object’s inertia, or resistance to motion.
• Force relative to resistance will determine if
the object will move or remain at rest.
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Kinds of Motion
• Although the variety of ways in which objects
move appears to be almost limitless, careful
consideration reveals only two classifications
of movement patterns:
– Translatory or linear
– Rotary or angular
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Translatory Movement
• An object is translated as a whole from one
location to another.
– Rectilinear: straight-line progression
– Curvilinear: curved translatory movement
Curvilinear
motion
Rectilinear
motion
Fig 11.1
Fig 11.2
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Circular Motion
• A special form of curvilinear motion.
• Object moves along the circumference of a
circle, a curved path of constant radius.
• The logic relates to the fact that an unbalanced
force acts on the object to keep it in a circle .
• If force stops acting on the object, it will move in
a linear path tangent to the direction of
movement when released.
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Rotary, or Angular, Motion
• Typical of levers,
wheels, & axles
• Object acting as a
radius moves about a
fixed point.
• Measured as an angle,
in degrees.
• Body parts move in an
arc about a fixed point.
Fig 11.3
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Rotary, or Angular, Motion
• Circular motion describes motion of any point
on the radius.
• Angular motion is descriptive of motion of the
entire radius.
• When a ball is held as the arm moves in a
windmill fashion
– ball is moving with circular motion.
– arm acts as a radius moving with angular
motion.
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Other Movement Patterns
• Combination of rotary & translatory is called
general motion
• Angular motions of forearm, upper arm & legs.
• Hand travels linearly and imparts linear force to
the foil
Fig 11.4
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Kinds of Motion
Experience by the Body
• Most joints are axial.
• Segments undergo
primarily angular
motion.
• Slight translatory
motion in gliding joints.
Fig 11.5
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Kinds of Motion
Experience by the Body
• Rectilinear movement when the body
is acted on by the force of gravity or a
linear external force
Fig 11.7
Fig 11.6
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Kinds of Motion
Experience by the Body
• General motion
– e.g. forward and backward rolls on ground
• Rotary motion
– e.g. spinning on ice skates
• Curvilinear translatory motion
– e.g. diving and jumping
• Reciprocating motion
– e.g. swinging on a swing
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Factors that Determine
the Kind of Motion
• Depends primarily on the kind of motion
permitted in a particular object.
– Lever permits only angular motion.
– Pendulum permits only oscillatory motion.
• If an object is freely movable, it permits either
translatory or rotary motion.
– Determined by where force is applied in
reference to its center of gravity.
– Presence or absence of modifying forces.
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Factors Modifying Motion
• External factors
– Friction helps a runner gain traction, but
hinders the rolling of a ball.
– Air resistance or wind is indispensable to
the sailboat’s motion, but may impede a
runner.
– Water resistance is essential for
propulsion, yet it hinders an objects’
progress through the water.
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Factors Modifying Motion
• Internal or anatomical factors:
– friction in joints; tension of antagonists,
ligaments & fasciae; anomalies of bone &
joint structure; atmospheric pressure inside
joints; and presence of interfering soft
tissues.
• One of the major problems in movement is
– How to take advantage of these factors.
– How to minimize them when they are
detrimental to the movement.
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KINEMATIC DESCRIPTION
OF MOTION
Linear Kinematics
• Distance
– How far an object has moved or traveled.
• Displacement
– Distance an object has moved from a
reference point.
– May not indicate how far object traveled.
– A vector quantity having both magnitude
and direction.
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Linear Kinematics
• Walk north 3 km, then east 4 km.
• What is the distance traveled?
• What is the displacement?
Fig 11.8
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Speed and Velocity
• Speed is how fast an object is moving,
nothing about the direction of movement.
– a scalar quantity
Average Speed = distance traveled or d
time
t
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Speed and Velocity
• Velocity involves direction as well as speed
– speed in a given direction
– rate of displacement
– a vector quantity
Average Velocity = displacement or s / t
time
v=s/t
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Acceleration
• The rate of change in velocity.
• May be positive or negative.
• If acceleration is positive then velocity will
increase.
• If acceleration is negative then velocity will
decrease.
Average acceleration = final velocity – initial velocity
time
a = (vf – vi)/t
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Acceleration
Fig 11.10
Section a:
Section b:
Section c:
Section d:
v- increasing (+)
v- constant (+)
v- non-linear increase (+)
v- decreasing (+)
a-constant (+)
a-zero
a- non-constant (+)
a- constant (-)
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Acceleration Units
a = (final velocity – initial velocity) / time
a = (final m/sec – initial m/sec) / sec
a = (m/sec) / sec
a = m/sec2
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Uniformly Accelerated Motion
•
•
•
•
Constant acceleration rate.
Common with freely falling objects.
Air resistance is neglected.
Objects will accelerate at a uniform rate due
to acceleration of gravity.
• Object projected upward will be slowed at
the same uniform rate due to gravity.
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Acceleration of Gravity
• 32 ft/sec2 or 9.8 m/sec2
• Velocity will increase 9.8 m/sec every second
when an object is dropped from some height.
– End of 1 sec = 9.8 m/sec
– End of 2 sec = 19.6 m/sec
– End of 3 sec = 29.4 m/sec
• Does not consider resistance or friction of air.
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Air Resistance
• Lighter objects will be affected more:
– may stop accelerating (feather) and fall at
a constant rate.
• Denser, heavier objects are affected less.
• Terminal velocity – air resistance is increased
to equal accelerating force of gravity.
– Object no longer accelerating, velocity
stays constant.
– Sky diver = approximately 120 mph or
53 m/sec.
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Laws of Uniformly
Accelerated Motion
• Distance traveled & downward velocity can
be determined for any point in time:
vf = vi + at
s = vi t + /2at2
vf 2 = vi 2 + 2as
Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time
s = displacement
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Laws of Uniformly
Accelerated Motion
• Time it takes for an object to rise to the
highest point of its trajectory is equal to the
time it takes to fall to its starting point.
• Upward flight is a mirror image of the
downward flight.
• Release & landing velocities are equal, but
opposite.
• Upwards velocities are positive.
• Downward velocities are negative.
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Projectiles
• Objects given an initial velocity and released.
• Gravity is the only influence after release.*
• Maximum horizontal displacement
– e.g. long jumper, shot-putter
• Maximum vertical displacement
– e.g. high jumper, pole vault
• Maximum accuracy
– e.g. shooting in basketball or soccer
* Neglecting air resistance.
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Projectiles
• Follows a predictable
path, a parabola.
• Gravity will
– slow upward motion.
– increase downward
motion.
– at 9.8 m/sec2
Fig 11.11
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Projectiles
Upward portion
Velocity versus Tim e
Upw ard
Velocity y-direction (m/s)
6
5
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
10
8
6
4
2
0
0
1.2
0.2
0.4
0.6
0.8
1
1.2
Time (sec)
Time (sec)
Acceleration versus Tim e
Upw ard
Acceleration y-direction
(m/s2)
Position y-direction (m)
Position versus Tim e
Upw ard
0
-2 0
0.2
0.4
0.6
0.8
1
1.2
-4
-6
-8
-10
-12
Time (sec)
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Projectiles
Downward portion
Velocity versus Tim e
Dow nw ard
Velocity y-direction (m/s)
6
5
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
1.2
0
-2
0
0.2
0.4
0.6
0.8
1
1.2
-4
-6
-8
-10
Time (sec)
Time (sec)
Acceleration versus Tim e
Dow nw ard
Acceleration y-direction
(m/s2)
Position y-direction (m)
Position versus Tim e
Dow nw ard
0
-2 0
0.2
0.4
0.6
0.8
1
1.2
-4
-6
-8
-10
-12
Time (sec)
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Projectiles
• Initial velocity at an angle of projection:
– Components
• Vertical velocity: affected by gravity
• Horizontal velocity: not affected by gravity
Fig 11.12
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Projectiles with
Horizontal Velocity
• One object fall as another object is projected
horizontally.
• Which will hit the ground first?
Gravity acts on both
objects equally
Horizontal velocity projects the
object some distance from the
release point
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Projectiles with
Vertical Velocity
• To affect time an object is in the air :
– vertical velocity must be added.
– height of release may be increased.
• Upward velocity will:
– be slowed by gravity.
– reach zero velocity.
– gain speed towards the ground.
– at height of release object will have the same
velocity it was given at release.
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Projectiles with Vertical and
Horizontal Velocities
• This is the case for most projectiles.
• Horizontal velocity remains constant.
• Vertical velocity subject to uniform acceleration
of gravity.
Fig 11.14
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Horizontal Distance
of a Projectile
• Depends on horizontal velocity & time of flight.
• Time of flight depends on maximum height
reached by the object.
– governed by vertical velocity of the object.
• Magnitude of these two vectors determined by:
– initial velocity vector.
– angle of projection.
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Angle of Projection
• Complementary angles of projection will have the
same landing point:
– A&B
– C&D
– 450 angle (E)
• Throwing events may have a lower angle of projection,
because of a difference in height of release and height
of landing.
Fig 11.15
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Factors that Control the
Range of a Projectile
1. Velocity of Release
2. Angle of Projection
3. Height of Release
4. Height at Landing
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Angular Kinematics
• Similar to linear kinematics.
• Also concerned with displacement, velocity,
and acceleration.
• Important difference is that they relate to
rotary rather than to linear motion.
• Equations are similar.
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Angular Displacement
• Skeleton is a system of levers that rotate
about fixed points when force is applied.
• Particles near axis have displacement less
than those farther away.
• Units of a circle:
– Circumference = C
C = 2πr
– Radius = r
– Constant (3.1416) = π
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Units of angular Displacement
• Degrees:
– Used most frequently
• Revolutions:
– 1 revolution = 360º = 2π radians
• Radians:
– 1 radian = 57.3°
– Favored by engineers & physicists
– Required for most equations
• Symbol for angular displacement -  (theta)
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Angular Velocity
=/t
• Rate of rotary displacement -  (omega).
• Equal to the angle through which the radius
turns divided by time.
• Expressed in degrees/sec, radians/sec, or
revolutions/sec.
• Called average velocity because angular
displacement is not always uniform.
• The longer the time span of the
measurement, the more variability is
averaged.
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Angular Velocity
• High-speed video:
• 150 frames / sec =
.0067 sec / picture
• Greater spacing, greater
velocity.
• “Instant” velocity
between two pictures:
a = 1432° / sec
b = 2864° /sec
Fig 11.16
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Angular
Acceleration
 = (f - i)/ t
•  (alpha) is the rate of change of angular
velocity and expressed by above equation.
– f is final velocity
– i is initial velocity
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Angular Acceleration
• a is 25 rad/sec
• b is 50 rad/sec
• Time lapse = 0.11 sec
Fig 11.16
 = f - i / t
 = (50 – 25) / 0.11
 = 241 rad/sec/sec
Velocity increases by 241
radians per sec each second.
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Relationship Between
Linear and Angular Motion
• Lever PA > PB > PC
• All move same angular distance in the same
time.
Fig 11.17
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Relationship Between
Linear and Angular Motion
•
•
•
•
Angular to linear displacement: s = r
C traveled farther than A or B, in the same time.
C had a greater linear velocity than A or B.
All three have the same angular velocity, but the linear
velocity of the circular motion is proportional to the
length of the lever.
• If angular distance is constant, the longer the
radius, the greater is the linear velocity of a
point at the end of that radius.
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Relationship Between
Linear and Angular Motion
• The reverse is also true.
• If linear velocity is constant, an increase in
radius will result in a decrease in angular
velocity, and vice versa.
Fig 11.18
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Relationship Between
Linear and Angular Motion
• If one starts a dive in an open position and
tucks tightly, angular velocity increases.
– Radius of rotation decreases.
– Linear velocity does not change.
• Shortening the radius will increase the
angular velocity, and lengthening it will
decrease the angular velocity.
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Relationship Between
Linear and Angular Motion
• The relationship between angular velocity and
linear velocity at the end of its radius is
 = r
expressed by
• Equation shows the direct proportionality that
exists between linear velocity and the radius.
© 2008 McGraw-Hill Higher Education. All Rights Reserved.
Chapter 11:
The Description of
Human Motion
© 2008 McGraw-Hill Higher Education. All Rights Reserved.