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Chapter 10
Linear Kinematics of Human Movement
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
© 2012 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
10-2
Linear Kinematic Quantities
How do we define kinematics?
• the pattern or sequencing of movement with respect to time
• the appearance of a motion
•Visually observable aspects of technique or form
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-3
Linear Kinematic Quantities
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
Movement kinematics is also referred to as form or technique.
10-4
Linear Kinematic Quantities
What is linear displacement?
• change in location
• the directed distance from initial to final location
• the vector equivalent of linear distance
• measured in units of cm, m, km
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-5
Linear Kinematic Quantities
The distance a skater travels may be measured from the track left on the ice. The skater’s displacement is measured in a straight line from start to finish.
Finish
Start
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
Path of distance traveled
displacement
10-6
Linear Kinematic Quantities
What is linear speed?
• distance covered over the time taken
distance • speed = time
• a scalar quantity m
• measured in units of s
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-7
Linear Kinematic Quantities
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
Running speed is the product of stride length and stride frequency.
10-8
Linear Kinematic Quantities
What is linear velocity?
• the rate of change in location
displacement d• velocity = time v = t
• the vector equivalent of linear speed m
• measured in units of s
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-9
Linear Kinematic Quantities
The velocity of a swimmer in a river is the vector sum of the velocities of swimmer and current.
Current velocity
Swimmer’s velocity
Resultant velocity
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-10
Linear Kinematic Quantities
What is acceleration?
• the rate of change in linear velocity
change in velocity • acceleration = time
v2-v1
• a = t m
• measured in units of s
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-11
Linear Kinematic Quantities
Acceleration may be positive, negative, or equal to zero, based on the direction of motion and the direction of the change in velocity.
Motion in a negative direction
Increasing speed
Decreasing speed
Negative acceleration
Positive acceleration
Motion in a positive direction
Increasing speed
Decreasing speed
Negative acceleration
Positive acceleration
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-12
Linear Kinematic Quantities
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
Sliding into base involves negative acceleration of the base runner.
10-13
Kinematics of Projectile Motion
What is a projectile?
(a body in free fall that is subject only to the forces of gravity and air resistance)
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-14
Kinematics of Projectile Motion
Why do we analyze the horizontal and vertical components of projectile motion separately?
(the vertical component is influenced by gravity and the horizontal
component is not)
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-15
Kinematics of Projectile Motion
Two balls - one dropped and one projected horizontally from the same height:
Both land at the same time since gravity affects their vertical velocities equally.
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-16
Kinematics of Projectile Motion
What is the effect of gravity?
(The force of gravity produces a constant acceleration of -9.81 m/s2 on bodies near the surface of the earth.)
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-17
Kinematics of Projectile Motion
The pattern of change in the
vertical velocity of a projectile is
symmetrical about the
apex.
Vertical velocity decreases as the ball rises and increases as the ball falls due to the influence of gravitational force.
apex
gravity
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-18
Factors Influencing Projectile Trajectory
What factors influence the trajectory (flight path) of a projectile?
• projection angle - the direction of projection with respect to the horizontal
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-19
Factors Influencing Projectile Trajectory
Max
imum
hei
ght
(m) 5
4
3
2
1
0
Range (distance) (m)0 1 2 3 4 5 6 7 8 9 10 11
This scaled diagram shows
the size and shape of
trajectories for an object
projected at 10 m/s at different
angles.
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-20
Factors Influencing Projectile Trajectory
The Effect of Projection Angle on Range(Relative Projection Height = 0)
Projection Projection Speed Angle Range (m/s) (degrees) (m) 10 10 3.49 10 20 6.55 10 30 8.83 10 40 10.04 10 45 10.19 10 50 10.04 10 60 8.83 10 70 6.55 10 80 3.49
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-21
Factors Influencing Projectile Trajectory
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
Projection angle is particularly important in shooting a basketball. A common error among novice players is shooting the ball with too flat a trajectory.
10-22
Factors Influencing Projectile Trajectory
What factors influence the trajectory (flight path) of a projectile?
• projection speed - the magnitude of projection velocity
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-23
Factors Influencing Projectile Trajectory
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
The instantaneous velocity of the shot at the moment of release primarily determines the ultimate horizontal displacement of the shot.
10-24
Factors Influencing Projectile Trajectory
What factors influence the trajectory (flight path) of a projectile?
• relative projection height - the difference between projection
height and landing heightBasic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
10-25
Factors Influencing Projectile Trajectory
FACTORS INFLUENCING PROJECTILE MOTION(Neglecting Air Resistance)
Variable Factors of InfluenceFlight time Initial vertical velocity
Relative projection heightHorizontal displacement Horizontal velocity
Relative projection heightVertical displacement Initial vertical velocity
Relative projection heightTrajectory Initial speed
Projection angleRelative projection height
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
10-26
Factors Influencing Projectile Trajectory
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.
The human body becomes a projectile during the airborne phase of a jump.
10-27
Analyzing Projectile Motion
The Equations of Constant Acceleration
These equations may be used to relate linear kinematic quantities whenever acceleration (a) is a constant, unchanging value.
2 = v1 + at (1)
d = v1t + ½ at2 (2)
v22 = v1
2 + 2ad (3)
v
Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.