CHAPTER 11:PART 2
THE DESCRIPTION OF
HUMAN MOTION
KINESIOLOGY
Scientific Basis of Human Motion, 12th edition
Hamilton, Weimar & Luttgens
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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-2
Angular Displacement
 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
C = 2πr
11B-3
Units of Angular Displacement
 Degrees:
 Used most frequently
 Revolutions:
 1 revolution = 360º = 2π radians
 Radians:
 1 radian = 57.3°
 Favored by engineers & physicists
 Required for most equations
 Symbol for angular displacement -  (theta)
11B-4
Angular Velocity


t
 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-5
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-6
Angular
 f   i 
or
Acceleration  
t
t
  (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-7
Angular Acceleration
 a is 25 rad/sec
 b is 50 rad/sec
 Time lapse = 0.11 sec
Fig 11.16
 f i

t
α = (50 – 25) /
0.11
α = 241 rad/sec/sec
Velocity increases by 241 rad/sec (13809 deg/sec) each
11B-8
second.
Relationship Between
Linear and Angular Motion
 Lever PA < PB < PC
 All move same angular distance in the same
time.
Fig 11.17
11B-9
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-10
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-11
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-12
Relationship Between
Linear and Angular Motion
 The relationship between angular velocity and
linear velocity at the end of its radius is
expressed by
 = r
 Equation shows the direct proportionality that
exists between linear velocity and the radius.
11B-13