# What is centripetal acceleration?

Dec 9, 2014

Centripetal acceleration is the acceleration of a body moving at constant speed along a circular path. The acceleration is directed inward toward the center of the circle. Its magnitude is equal to the body's speed squared divided by the radius between the body and the center of the circle. Note: Even though the speed is constant, the velocity is not, because the direction of the body is changing constantly.

$\text{a}$ = $\text{v"^2/"r}$

$\text{a}$ = centripetal acceleration
$\text{r}$ = circular radius
$\text{v}$ = velocity

Example.

Q. A car moving at a speed of 29.0 m/s moves around a circle with a radius of 20.0 m. Determine the acceleration of the car.
r = 20.0 m, v = 29.0 m/s

A. $\text{a}$ = $\text{v"^2/"r}$= $\text{(29.0 m/s)(29.0 m/s)"/"20.0 m}$ = ${\text{42.1 m/s}}^{2}$