The frequency of an object in circular motion is determined by its angular velocity.

Angular velocity quantifies how rapidly an object rotates around a fixed point, such as the center of a circle. This measurement is expressed in radians per second ($\text{rad/s}$). The frequency of the object’s motion refers to the number of complete rotations it performs per second, which is measured in hertz ($\text{Hz}$).

To calculate the frequency of an object in circular motion, we need to know both its angular velocity and the circumference of the circle in which it is moving. The formula for frequency is given by:

In this equation, $f$ represents the frequency, $v$ is the angular velocity, and $r$ is the radius of the circle.

For instance, consider an object that rotates around a circle with a radius of $0.5$ meters and has an angular velocity of $2$ radians per second. We can calculate its frequency as follows:

This result indicates that the object completes approximately $0.637$ full rotations per second.