Derive the formula $a_c = R\omega^2$ from $a_c = \frac{v^2}{R}$.

(N/A) We are given the centripetal acceleration formula as $a_c = \frac{v^2}{R}$.
We know the relationship between linear velocity $v$ and angular velocity $\omega$ is given by $v = R\omega$,where $R$ is the radius of the circular path.
Substitute $v = R\omega$ into the centripetal acceleration formula:
$a_c = \frac{(R\omega)^2}{R}$
$a_c = \frac{R^2\omega^2}{R}$
By simplifying the expression,we get:
$a_c = R\omega^2$.