# Centripetal Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Centripetal acceleration is the change in the velocity, which is a vector, either in speed or direction as an object makes its way around a circular path.  Abbreviated ac, centripetal acceleration points towards the center of the circular path that keeps an object in an elliptical orbit with the direction of the velocity vector constantly changing.

### Centripetal Acceleration Formula

Eq. 1:   $$\large{ a_c = \frac { v^2 } { r } }$$

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

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

Where:

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

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

$$\large{ r }$$ = radius

$$\large{ v }$$ = velocity

Solve for:

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

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