CHAPTER 11:PART 2CHAPTER 11:PART 2THE DESCRIPTION OF THE DESCRIPTION OF

HUMAN MOTIONHUMAN MOTION

CHAPTER 11:PART 2CHAPTER 11:PART 2THE DESCRIPTION OF THE DESCRIPTION OF

HUMAN MOTIONHUMAN MOTION

KINESIOLOGYScientific Basis of Human Motion, 12th edition

Hamilton, Weimar & LuttgensPresentation Created by

TK Koesterer, Ph.D., ATCHumboldt State University

Revised by Hamilton & Weimar

Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

11B-2

Angular KinematicsAngular 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 = CRadius = rConstant (3.1416) = π

Angular DisplacementAngular Displacement

C = 2πr

11B-4

Units of Angular DisplacementUnits of Angular DisplacementDegrees:

Used most frequently

Revolutions:1 revolution = 360º = 2π radians

Radians: 1 radian = 57.3°

Favored by engineers & physicistsRequired for most equations

Symbol for angular displacement - (theta)

11B-5

Angular VelocityAngular 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.

t

11B-6

Angular VelocityAngular 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 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

f i

tor

t

11B-8

Angular Acceleration Angular Acceleration

a is 25 rad/sec

b is 50 rad/sec

Time lapse = 0.11 secFig 11.16

α = (50 – 25) / 0.11α = 241 rad/sec/sec

Velocity increases by 241 rad/sec (13809 deg/sec) each second.

f i

t

11B-9

Relationship Between Linear and Angular MotionRelationship Between Linear and Angular MotionLever PA < PB < PC

All move same angular distance in the same time.

Fig 11.17

11B-10

Relationship Between Linear and Angular MotionRelationship Between Linear and Angular MotionAngular 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 MotionRelationship Between Linear and Angular MotionThe 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 MotionRelationship Between Linear and Angular MotionIf 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 MotionRelationship 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