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.
$\vecphy{\theta}$, angular velocity $\vecphy{\omega}$, velocity $\vecphy{v}$ and radius $r$" src="https://www.toktol.com//Content/images/transparent.gif" onload="conditionalLoadImage(this, 'https://toktolweb.blob.core.windows.net/courseimages/', 'Physics.AL.NM.CM.01.png', false, {}, 'https://toktolwebcdn.blob.core.windows.net/quizimages/')" name="Physics.AL.NM.CM.01.png" sub="An object moving in uniform circular motion with angular displacement $\vecphy{\theta}$, angular velocity $\vecphy{\omega}$, velocity $\vecphy{v}$ and radius $r$" />
An object moving in uniform circular motion with angular displacement $\vecphy{\theta}$, angular velocity $\vecphy{\omega}$, velocity $\vecphy{v}$ and radius $r$