A.2.23—Centripetal acceleration

Radial acceleration

For uniform circular motion, the centripetal acceleration is directed toward the centre:

$$a_c=\frac{v^2}{r}=\omega^2r=\frac{4\pi^2r}{T^2}$$

Velocity can be constant in magnitude

Even when speed is constant, the velocity direction changes continuously. That directional change produces inward acceleration.

Choose the matching data

Use $v^2/r$ when speed and radius are given, $\omega^2r$ when angular speed is given, or $4\pi^2r/T^2$ when period is given.

Common trap

Centripetal acceleration is not tangential and does not point along the instantaneous velocity.