Angular Period
Angular period, T, is defined as the time required to complete one revolution and is related to
frequency by the equation:
Since we know that the frequency of the second hand is^1 / 60 Hz, we can quickly see that the period
of the second hand is 60 s. It takes 60 seconds for the second hand to complete a revolution, so the
period of the second hand is 60 seconds. Period and angular velocity are related by the equation
EXAMPLE
The Earth makes a complete rotation around the sun once every 365.25 days. What is the Earth’s
angular velocity?The question tells us that the Earth has a period of T = 365. 25 days. If we plug this value into the
equation relating period and angular velocity, we find:
Note, however, that this equation only gives us the Earth’s angular velocity in terms of radians per
day. In terms of radians per second, the correct answer is:
Relation of Angular Variables to Linear Variables
At any given moment, a rotating particle has an instantaneous linear velocity and an instantaneous
linear acceleration. For instance, a particle P that is rotating counterclockwise will have an
instantaneous velocity in the positive y direction at the moment it is at the positive x-axis. In
general, a rotating particle has an instantaneous velocity that is tangent to the circle described by
its rotation and an instantaneous acceleration that points toward the center of the circle.
On SAT II Physics, you may be called upon to determine a particle’s linear velocity or