Centripetal acceleration
= Centripetal acceleration
{title2=$\mathbf a=-\omega^2\mathbf r$}
For uniform <circular motion> of radius $R$ and <angular speed> $\omega$, the <acceleration> is directed toward the centre and has magnitude $\omega^2R=v^2/R$. Writing $\mathbf r$ for the <position> relative to the centre gives $\ddot{\mathbf r}=-\omega^2\mathbf r$. The required resultant <force> is $m\ddot{\mathbf r}$; it may be supplied by a <normal force>, gravity, or another physical interaction.