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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.

An object moving in uniform circular motion with angular displacement <span style=$$\vecphy{\theta}$$, 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 $$r$$