# CENTRIPETAL ACCELERATION FORMULA

The centripetal acceleration formula is

ac=v2/r = w2r

where ac is centripetal acceleration, v is speed and r is radius of the circular path.

In uniform circular motion, the direction of velocity vector is continuously changing but the magnitude of the velocity vector (or speed) is constant. Since the velocity vector is changing, there must be an acceleration responsible from this change. The centripetal acceleration is the acceleration that changes the velocity of an object in circular path. Centripetal acceleration is a vector quantity and always perpendicular to velocity vector, and the direction of centripetal acceleration is toward the center of the circular path.

The centripetal acceleration is linearly proportional with r. Let’s think about a disc which is rotating with constant angular velocity w. Suppose that someone starts to walk on that disc from the center. At the center of the disc the centripetal acceleration, that the person experiences, will be zero because r is zero. The centripetal acceleration will increase when the person walks out to the edge of the disc because r is getting larger (r1<r2).

## Centripetal Acceleration Example

A child sitting 1.50 m away from the center of a carousel moves with a speed of 1 m/s. Calculate the centripetal acceleration of the child.

Solution:  The centripetal acceleration formula is ac =v2/r. Radius of the circle is 1.5 m and the speed of the child is 1 m/s. The centripetal acceleration is

ac =v2/r

ac =(1 m/s)2/(1.5m)

ac = 0.67 m/s2