Acceleration of Particle moving in Circle

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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.


Proof


Sources