# Centripetal Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Centripetal Acceleration

Centripetal acceleration ( $$a_c$$ ) is acceleration towards the center that keeps an object in an elliptical orbit with the direction of the velocity vector constantly changing.

### Centripetal Acceleration Formula

$$\large{ a_c = \frac { v^2 } { r } }$$

$$\large{ a_c = \frac { \left( r \omega \right) ^2 } { r } }$$

$$\large{ a_c = r \omega^2 }$$

Where:

$$\large{ a_c }$$ = centripetal acceleration

$$\large{ r }$$ = radius

$$\large{ v }$$ = velocity

$$\large{ \omega }$$  (Greek symbol omega) = angular velocity

Solve for:

$$\large{ v = \sqrt { a r } }$$

$$\large{ r = \frac { v^2 } { a } }$$