Acceleration of Particle moving in Circle

Theorem
Let $P$ be a particle moving in a circular path $C$.

Then the acceleration of $P$ is given as:


 * $\mathbf a = \dfrac {\size {\mathbf v}^2 \mathbf r} {\size {\mathbf r}^2}$

where:
 * $\mathbf v$ is the instantaneous velocity of $P$
 * $\mathbf r$ is the vector whose magnitude equals the length of the radius of $C$ and whose direction is toward the center of $C$
 * $\size {\, \cdot \,}$ denotes the magnitude of a vector.