1. Angular Kinematics of Human Movement
Chapter 11
Angular Kinematics of Human Movement
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
© 2012 The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

2. Basic Biomechanics, 6th edition
Measuring Angles
What is a relative angle?
angle at a joint formed between the longitudinal axes of adjacent body segments
AKA joint angle
the straight, fully extended position at a joint is regarded as zero degrees
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

3. Basic Biomechanics, 6th edition
Measuring Angles
The relative angle at the lead knee tends to be smaller during sprinting than during distance running.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

4. Basic Biomechanics, 6th edition
Measuring Angles
What is an absolute angle?
angular orientation of a body segment with respect to a fixed line of reference
(reference lines are usually vertical or horizontal)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

5. Basic Biomechanics, 6th edition
Measuring Angles
The absolute angle of the trunk with respect to vertical is often a quantity of interest in studies of lifting as related to low back pain.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

6. Angular Kinematic Quantities
What is angular displacement?
change in angular position
the directed angular distance from initial to final angular position
the vector equivalent of angular distance
measured in units of degrees, radians, or rotations
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

7. Angular Kinematic Quantities
What is a radian?
radius
1 radian
The size of the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

8. Angular Kinematic Quantities
Units of angular measure
90 degrees
radians
revolution 2 14
180 degrees  12
270 degrees
3 2 34
360 degrees
1revolution 2
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

9. Angular Kinematic Quantities
What is angular velocity?
the rate of change in angular position
angular displacement angular velocity = time 
 = t
degrees radians
measured in units of s or s
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

10. Angular Kinematic Quantities
What is angular acceleration?
the rate of change in angular velocity
 ang.velocity
angular acceleration = time
2 - 1
 = t
deg rad
measured in units of s or s
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

11. Relationships Between Linear and Angular Motion
What is the relationship between linear and angular displacement?
The greater the radius between a given point on a rotating body and the axis of rotation, the greater the linear distance traveled by that point during an angular motion.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

12.  Relationships Between Linear and Angular Motion r1 r2 s2 s1 
The larger the radius of rotation (r), the greater the linear distance (s) traveled by a point on a rotating body.
s = r
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

13. Relationships Between Linear and Angular Motion
What is the relationship between linear and angular velocity?
Since velocity is displacement over time, linear and angular velocity are related by the same factor that relates displacement: the radius of rotation (r).
v = r
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

14. Relationships Between Linear and Angular Motion
What is the relationship between linear and angular acceleration?
The acceleration of a body in angular motion can be resolved into two perpendicular linear acceleration components.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

15. Relationships Between Linear and Angular Motion
What is tangential acceleration?
component of acceleration of angular motion directed along a tangent to the path of motion
represents change in linear speed
v2 - v1
at = t at
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

16. Relationships Between Linear and Angular Motion
What is radial acceleration?
component of acceleration of angular motion directed toward the center of curvature
represents change in direction v2
ar = t ar
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.