# Period and frequency of circular motion

The period $$(T)$$ of circular motion is the time taken for an object undergoing circular motion to complete **one full revolution** of the circle.

The frequency $$(f)$$ of circular motion is the **number of revolutions** completed by the object per second. It is related to the period by:$$$f=\frac{1}{T}$$$The **SI unit** of frequency is **Hertz $$(\text{Hz})$$**. The unit of Hertz is equivalent to one inverse second (i.e. $$1\text{ Hz}=1\text{ s}^{-1}$$).

The angular speed $$\omega$$ can be obtained from the period and frequency by:$$$\omega=\frac{2\pi}{T}=2\pi f$$$This formula is derived from the formula $$\omega=\theta/t$$ by taking $$\theta=2\pi$$ (one revolution) as the angle and $$t=T$$ (one period) as the time. This formula only holds for objects undergoing **uniform circular motion**.