The frequency of circular motion is directly proportional to angular velocity.

When an object travels along a circular path, it experiences circular motion. The frequency of this motion, denoted as $f$, is defined as the number of complete revolutions the object makes in one second. In contrast, the angular velocity, represented by $\omega$, is the rate at which the angular displacement changes with respect to time, measured in radians per second.

The relationship between the frequency of circular motion and angular velocity is expressed by the equation:

In this equation, $f$ is the frequency, and $\omega$ is the angular velocity. This formula illustrates that the frequency of circular motion is directly proportional to angular velocity. Therefore, an increase in angular velocity results in a corresponding increase in the frequency of circular motion.

To further understand this relationship, we can consider the concept of the period, denoted as $T$. The period of circular motion is the time required for the object to complete one full revolution, and it is given by the equation:

Substituting this into the frequency equation, we can rewrite it as:

This formulation shows that the period of circular motion is inversely proportional to the angular velocity. Hence, as the angular velocity increases, the period of the circular motion decreases.

In summary, the frequency of circular motion is directly proportional to angular velocity, while the period is inversely proportional to angular velocity. These relationships highlight the interconnectedness of these fundamental concepts in circular motion.