CHAPTER 11:PART 2 THE DESCRIPTION OF HUMAN MOTION KINESIOLOGY Scientific Basis of Human Motion, 12 th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Revised by Hamilton & Weimar Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

11B-2 Angular Kinematics Similar to linear kinematics. Also concerned with displacement, velocity, and acceleration. Important difference is that they relate to angular rather than to linear motion. Equations are similar.

11B-3 Skeleton is a system of levers that rotate about fixed points when force is applied. Particles near axis have less displacement than those farther away. Units of a circle: Circumference = C Radius = r Constant (3.1416) = π Angular Displacement C = 2 πr

11B-4 Units of Angular Displacement Degrees: Used most frequently Revolutions: 1 revolution = 360 º = 2π radians Radians: 1 radian = 57.3 ° Favored by engineers & physicists Required for most equations Symbol for angular displacement -  (theta)

11B-5 Angular Velocity 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.

11B-6 Angular Velocity High-speed video: 150 frames / sec =.0067 sec / picture Greater spacing, greater velocity. “Instant” velocity between two pictures: a = 1432 ° / sec (25 rad/sec) b = 2864 ° /sec (50 rad/sec) Fig 11.16

11B-7 Angular Acceleration  (alpha) is the rate of change of angular velocity and expressed by above equation.  f is final velocity  i is initial velocity Δ is change in velocity

11B-8 Angular Acceleration  a is 25 rad/sec  b is 50 rad/sec Time lapse = 0.11 sec Fig α = (50 – 25) / 0.11 α = 241 rad/sec/sec Velocity increases by 241 rad/sec (13809 deg/sec) each second.

11B-9 Relationship Between Linear and Angular Motion Lever PA < PB < PC All move same angular distance in the same time. Fig 11.17

11B-10 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. The longer the radius, the greater the linear velocity of a point at the end of that radius.

11B-11 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

11B-12 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.

11B-13 Relationship Between Linear and Angular Motion The relationship between angular velocity and linear velocity at the end of its radius is expressed by Equation shows the direct proportionality that exists between linear velocity and the radius. =  r