Period and Frequency in Circular Motion

When an object moves in a circle, we measure how fast it revolves using two related quantities.

Period ($T$): The time it takes to complete one full revolution, measured in seconds.

Frequency ($f$): The number of revolutions per second, measured in hertz (Hz). One Hz means one revolution per second. Since frequency has units of $\text{Hz} = \dfrac{1}{\text{s}} = \text{s}^{-1}$, it has dimensions of inverse time.

The relationship: Period and frequency are inversely related:

A short period (fast motion) means high frequency. A long period (slow motion) means low frequency.

Example 1: Fast rotation with $T = 0.25$ s

The frequency is $f = \frac{1}{0.25} = 4$ Hz (four revolutions per second).

Example 2: Slow rotation with $f = 0.5$ Hz

The period is $T = \frac{1}{0.5} = 2$ s per revolution.