Formula: Circular motion Angular velocity Radius Mass
$$F_{\text z} ~=~ \class{brown}{m} \, {\class{red}{\omega}}^2 \, r$$
$$F_{\text z} ~=~ \class{brown}{m} \, {\class{red}{\omega}}^2 \, r$$
$$\class{red}{\omega} ~=~ \sqrt{ \frac{F_{\text z}}{\class{brown}{m}\, r} } $$
$$r ~=~ \frac{F_{\text z}}{\class{brown}{m} \, {\class{red}{\omega}}^2}$$
$$\class{brown}{m} ~=~ \frac{F_{\text z}}{r \, {\class{red}{\omega}}^2}$$
Centripetal force
$$ F_{\text z} $$ Unit $$ \mathrm{N} $$
Centripetal force (also called radial force) is a force acting on a body rotating in a circle (towards the center of the circle). This force keeps the body on the circular orbit. It is always perpendicular to the angular velocity \(\omega\) in a uniform circular motion.
Angular velocity
$$ \class{red}{\omega} $$ Unit $$ \frac{\mathrm{rad}}{\mathrm s} $$
Angular velocity indicates which angle is traveled by the body per second. If \(\omega\) is doubled, then the centripetal force \( F_{\text z} \) is quadrupled.
Radius
$$ r $$ Unit $$ \mathrm{m} $$
Radius of the circular trajectory. If the radius is doubled (at constant angular velocity), then the centripetal force is also doubled.
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Mass of the body moving on the circular path. Heavier bodies require a larger centripetal force to keep them on the circular path with a certain radius.