Formula: Circular Motion Centripetal acceleration Radius Angular velocity
$$a_{ \text z } ~=~ {\class{red}{\omega}}^2 \, r$$
$$a_{ \text z } ~=~ {\class{red}{\omega}}^2 \, r$$
$$r ~=~ \frac{a_{ \text z }}{{\class{red}{\omega}}^2}
$$
$$\class{red}{\omega} ~=~ \sqrt{\frac{a_{ \text z }}{r}}
$$
Centripetal acceleration
$$ a_{\text z} $$ Unit $$ \frac{\mathrm{m}}{\mathrm{s}^2} $$
Acceleration, which a body (e.g. a planet, a particle) experiences, which moves on a circular path. The centripetal acceleration points like the centripetal force to the circle center (in radial direction).
Radius
$$ r $$ Unit $$ \mathrm{m} $$
Radius of the circular path. This is the distance from the center of the circle to the rotating body.
Angular velocity
$$ \class{red}{\omega} $$ Unit $$ \frac{\mathrm{rad}}{\mathrm s} $$
Angular velocity (angular frequency) indicates which angle is covered by the body per second. If \(\omega\) is doubled, then the centripetal acceleration \( a_{\text z} \) is quadrupled.