Chapter 10 Linear Kinematics of Human Movement Basic

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, 6 th edition By Susan J. Hall, Ph. D. 10 -2

Linear Kinematic Quantities Movement kinematics is also referred to as form or technique. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -3

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, 6 th edition By Susan J. Hall, Ph. D. 10 -4

Linear Kinematic Quantities Path of distance traveled Finish Start displacement 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. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -5

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, 6 th edition By Susan J. Hall, Ph. D. 10 -6

Linear Kinematic Quantities Running speed is the product of stride length and stride frequency. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -7

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, 6 th edition By Susan J. Hall, Ph. D. 10 -8

Linear Kinematic Quantities Current velocity Swimmer’s velocity Resultant velocity The velocity of a swimmer in a river is the vector sum of the velocities of swimmer and current. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -9

Linear Kinematic Quantities What is acceleration? • the rate of change in linear velocity change in velocity • acceleration = time v 2 -v 1 • a= t m • measured in units of s 2 Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -10

Linear Kinematic Quantities Increasing speed Positive acceleration Negative acceleration Decreasing speed Negative acceleration Positive acceleration Motion in a negative direction Motion in a positive direction Acceleration may be positive, negative, or equal to zero, based on the direction of motion and the direction of the change in velocity. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -11

Linear Kinematic Quantities Sliding into base involves negative acceleration of the base runner. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -12

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, 6 th edition By Susan J. Hall, Ph. D. 10 -13

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, 6 th edition By Susan J. Hall, Ph. D. 10 -14

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, 6 th edition By Susan J. Hall, Ph. D. 10 -15

Kinematics of Projectile Motion What is the effect of gravity? (The force of gravity produces a constant acceleration of -9. 81 m/s 2 on bodies near the surface of the earth. ) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -16

Kinematics of Projectile Motion The pattern of change in the vertical velocity of a projectile is symmetrical about the apex gravity Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. Vertical velocity decreases as the ball rises and increases as the ball falls due to the influence of gravitational force. 10 -17

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, 6 th edition By Susan J. Hall, Ph. D. 10 -18

This scaled diagram shows the size and shape of trajectories for an object projected at 10 m/s at different angles. Maximum height (m) Factors Influencing Projectile Trajectory 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 Range (distance) (m) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -19

Factors Influencing Projectile Trajectory The Effect of Projection Angle on Range (Relative Projection Height = 0) Projection Speed Angle Range (m/s) (degrees) (m) 10 10 10 20 30 40 45 50 60 70 80 Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 3. 49 6. 55 8. 83 10. 04 10. 19 10. 04 8. 83 6. 55 3. 49 10 -20

Factors Influencing Projectile Trajectory Projection angle is particularly important in shooting a basketball. A common error among novice players is shooting the ball with too flat a trajectory. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -21

Factors Influencing Projectile Trajectory What factors influence the trajectory (flight path) of a projectile? • projection speed - the magnitude of projection velocity Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -22

Factors Influencing Projectile Trajectory The instantaneous velocity of the shot at the moment of release primarily determines the ultimate horizontal displacement of the shot. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -23

Factors Influencing Projectile Trajectory What factors influence the trajectory (flight path) of a projectile? • relative projection height - the difference between projection height and landing height Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -24

Factors Influencing Projectile Trajectory FACTORS INFLUENCING PROJECTILE MOTION (Neglecting Air Resistance) Variable Factors of Influence Initial vertical velocity Flight time Relative projection height Horizontal velocity Horizontal displacement Relative projection height Initial vertical velocity Vertical displacement Relative projection height Trajectory Initial speed Projection angle Relative projection height Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -25

Factors Influencing Projectile Trajectory The human body becomes a projectile during the airborne phase of a jump. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -26

Analyzing Projectile Motion The Equations of Constant Acceleration v 2 = v 1 + at (1) d = v 1 t + ½ at 2 (2) v 22 = v 12 + 2 ad (3) These equations may be used to relate linear kinematic quantities whenever acceleration (a) is a constant, unchanging value. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph. D. 10 -27