relative position to one another. As a result, the angular displacement is the same for every point in
a rotating rigid body.
Also note that the angular distance a point has rotated may or may not equal that point’s angular
displacement. For example, if you rotate a record 45º clockwise and then 20º counterclockwise,
the angular displacement of the record is 25º, although the particles have traveled a total angular
distance of 65º. Hopefully, you’ve already had it hammered into your head that distance and
displacement are not the same thing: well, the same distinction applies with angular distance and
angular displacement.
Angular Velocity
Angular velocity, , is defined as the change in the angular displacement over time. Average
angular velocity, , is defined by:
Angular velocity is typically given in units of rad/s. As with angular displacement, the angular
velocity of every point on a rotating object is identical.
Angular Acceleration
Angular acceleration, , is defined as the rate of change of angular velocity over time. Average
angular acceleration, , is defined by:
Angular acceleration is typically given in units of rad/s^2.
Frequency and Period
You’ve encountered frequency and period when dealing with springs and simple harmonic motion,
and you will encounter them again in the chapter on waves. These terms are also relevant to
rotational motion, and SAT II Physics has been known to test the relation between angular velocity
and angular frequency and period.
Angular Frequency
Angular frequency, f, is defined as the number of circular revolutions in a given time interval. It
is commonly measured in units of Hertz (Hz), where 1 Hz = 1 s–1. For example, the second hand
on a clock completes one revolution every 60 seconds and therefore has an angular frequency of^1
/ 60 Hz.
The relationship between frequency and angular velocity is:
For example, the second hand of a clock has an angular velocity of s.
Plugging that value into the equation above, we get
which we already determined to be the frequency of the second hand of a clock.