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Formulae for centripetal force and acceleration

A simple expression for the magnitude of centripetal force follows from Newton's second law:$$$\begin{align*}F=ma=\frac{mv^{2}}{r}=mr\omega^{2}\end{align*}$$$The variable $$a$$ is the magnitude of centripetal acceleration (i.e. acceleration directed towards the centre). It is given by:$$$\begin{align*}a&=\frac{v^{2}}{r}=r\omega^{2}\end{align*}$$$

$$v=$$linear speed; $$\omega=$$angular speed; $$r=$$radius of circular motion.

An object moving in uniform circular motion with angular displacement <span style=$$\vecphy{\theta}$$, angular velocity $$\vecphy{\omega}$$, speed $$\vecphy{v}$$ 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 $$\vecphy{\omega}$$, speed $$\vecphy{v}$$ and radius $$r$$" />
An object moving in uniform circular motion with angular displacement $$\vecphy{\theta}$$, angular velocity $$\vecphy{\omega}$$, speed $$\vecphy{v}$$ and radius $$r$$