5.2: Centripetal Force

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When you’re rotating at constant angular velocity, the magnitude of your velocity is always the same, but its direction constantly changes - so you’re constantly undergoing an acceleration, as indicated in Equation 5.1.6. Therefore there must be a net force acting on you. We can calculate that net force using Newton’s second law of motion. It is known as the centripetal force and given by:

\[\boldsymbol{F}_{\mathrm{cp}}=m \boldsymbol{a}=-\frac{m v^{2}}{r} \boldsymbol{\hat{r}}=-m \omega^{2} r \boldsymbol{\hat{r}} \label{special2ndlaw}\]

‘Centripetal’ means ‘center-seeking’ (from Latin ‘centrum’ = center and ‘petere’ = to seek). It is important to remember that this is a net resulting force, not a ‘new’ force like that exerted by gravity or a compressed spring. Equation \ref{special2ndlaw} is after all just a special case of Newton’s second law of motion.