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Angular Kinematics

Angular Kinematics. Today…. Distinguish angular motion from linear Discuss the relationship among angular kinematic variables Examine the relationships between angular and linear displacement, velocity and acceleration. Introduction. Why is a driver longer than a 9 iron?

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Angular Kinematics

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  1. Angular Kinematics

  2. Today…. • Distinguish angular motion from linear • Discuss the relationship among angular kinematic variables • Examine the relationships between angular and linear displacement, velocity and acceleration

  3. Introduction • Why is a driver longer than a 9 iron? • Why do batters slide their hands up the handle of the bat to execute a bunt but not a power hit?

  4. Angular motion • Most human movement involves rotation of body segment(s) • Gait = translation (linear) • Gait occurs because of rotational motions at the hip, knee & ankle

  5. Measuring angles • Angle = 2 sides that intersect at a vertex • Measure of angle and change in angle position = quantitative kinematic analysis

  6. Angles • Relative angle: angle at joint formed between long axes of adjacent body segments • Absolute angle: angular orientation of a segment with respect to a fixed line of reference • Angle of inclination of the trunk

  7. Angles • Anatomical position • ALL joint angles = 0°

  8. Angles • Absolute angle uses: • Trunk inclination in a runner • Technique • ? Effect on required extensor torque

  9. Angular Kinematics Angular relationships

  10. Angular Relationships • Similar relationships as linear • Units of measure differ

  11. Angular distance & displacement • Pendulum swings through arc of 60° • Distance = ? • If swings back through 60° • Distance = ? • Angular distance is the sum of all angular changes of a rotating body 60°

  12. Angular distance & displacement • Biceps curls: • 0° to 140° : distance = 140° • Return to 0° total distance = 280° • Repeat 10X  total distance = 2800° What is the displacement?

  13. Angular displacement • The change in angular position of a line/segment • The difference in the initial & final positions of the moving body • Biceps curl example: 0° – 140° & return • Displacement?

  14. Angular displacement • Defined by magnitude and direction • Clockwise (-) & counterclockwise (+) • Flexion & extension terms as well •  • Units • Degrees • Radian: 1 radian = 57.3° • Size of angle at the center of a circle by an arc equal in length to the radius • Often expressed in multiples of  • Revolution: used in diving & gymnastics +

  15. Degrees, rads & revolutions

  16. Angular speed Angular distance/time  =  / tf - ti Angular velocity Angular displacement / change in time  =  / tf – ti include positive or negative direction Units: °/s, rad/s, rpm Angular speed & velocity

  17. Applications of angular velocity • Baseball pitchers: 6000+°/s during acceleration (IR) 4500+°/s elbow extension • Tennis racket: during serve: 2000°/s to 2200°/s • Skaters: # of revolutions determined by jump height or rotational velocity

  18. Applications of angular velocity • Gymnasts: • Handsprings: 6.80 rad/s • Handspring w/somersault & ½ twist: 7.77 rad/s • Back layout: 10.2 rad/s

  19. Angular acceleration • Rate of change of angular velocity  = /t • Units: °/s2, rad/s2, rev/s2

  20. Relationships between linear & angular displacement • The greater the radius between a given point on a rotating body and the axis or rotation…… …the greater the linear distance the point moves during angular motion s2 2 2 s1 1 1 r2 r1 

  21. Relationships between linear & angular displacement • Formula s = r r = radius of rotation  = angular distance (in rads) **linear distance & radius of rotation must be in the same units of length **angular distance must be in rads

  22. Relationships between linear & angular velocity • Similar relationship v = r v = tangential velocity r = radius of rotation  = angular velocity **rads are not balanced on both sides of the equation 30 cm 20 cm

  23. Relationships between linear & angular velocity …the greater the radius of rotation… ……the greater the linear velocity ? Length of implements vs weight of implements (control) Linear velocity of ball  velocity of implement

  24. Relationships between linear & angular acceleration • Two perpendicular linear acceleration components 1. Along path of angular motion (tangential acceleration) 2. Perpendicular to path of angular motion (radial acceleration) at ar

  25. Relationships between linear & angular acceleration • Tangential: at = v2 – v1/t at = r • Radial: ar = v2/r

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