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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.

$\vecphy{\theta}$, 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 $r$