Ch. 11 - Angular Kinematics of Human Movement

Relative angle

angle at a joint formed between the longitudinal axes of adjacent body segments

(ex: the relative angle of the knee tends to be smaller during sprinting than during distance running)

Absolute angle

Angular orientation of a body segment with respect to a fixed line of reference

reference lines are usually vertical or horizontal

(ex: 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)

Angular distance

actual sum of all angular changes undergone by a rotating body

Angular displacement

change in angular position or orientation of a line segment

What is a 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

90 degrees =
_____ radians?
_____ revolutions?

pi/2 rad

1/4 rev

180 degrees =
_____ radians?
_____ revolutions?

pi rad

1/2 rev

270 degrees =
_____ radians?
_____ revolutions?

3pi/2 rad

3/4 rev

360 degrees =
_____ radians?
_____ revolutions?

2pi rad

1 rev

Angular velocity

rate of change in angular displacement

w = theta/t

deg/s or rad/s

Angular acceleration

rate of change in angular velocity

a = (w1 - w2)/ t

deg/s or rad/s

What is the relationship between linear and angular displacement?

The larger the radius of rotation (r), the greater the linear distance (s) traveled by a point on a rotating body

s = r(theta)

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

v = rw

How is tangential acceleration represented in angular motion?

What does the line represent? Give a formula

perpendicular line directed along a path tangent to the path of motion

represents change in linear speed

at = v2-v1/ t

What is radial acceleration? How is it represented along a path of motion?

What does this represent? Give a formula

component of acceleration of angular motion, directed toward the center of the curvature

represents change in direction

ar = v^2/t