# Centripetal Acceleration Definition

**Centripetal acceleration** is defined as the **acceleration** that is **directed radially** towards the **center of a circle** having a **magnitude** **equal **to the **squared velocity** of the body along a curve, **divided by the total distance** from the center. Whereas if an object moves radially away from the center, then a force pushing an object back and tends it to rotate around an axis of rotation is the centripetal force.

For instance, if an object is rotating around an axis of rotation, then you can determine the centripetal acceleration by calculating the square of velocity** **at which an object is rotating divided by the total radius between an object and a center (also known as the axis of rotation). The unit used to symbolize centripetal acceleration is m/s^{2}.

**Table of Contents**

## Formula of Centripetal Acceleration

To determine centripetal acceleration, you can use the formula listed below; or you can find your solutions instantly by using our free online centripetal calculator.

a_{c }= v^{2}/ r

**Where,**

a_{c} = The centripetal acceleration of an object

v = velocity of an object

r = radius between object and center

**Note:**

To calculate the centripetal acceleration, you can use our Centripetal Acceleration Calculator.

### Example

For a more precise understanding of the concept of centripetal acceleration, let us solve an example below:

Suppose if a cart is rotating in a roundabout with a velocity of 25m/s, whereas the radius of a roundabout is 15m. Then determine the centripetal acceleration of a moving object.

**Given data**

Velocity = v = 25 m/s

Radius = r = 15m

**To Find**

The centripetal acceleration = ?

**Solution**

To find out the centripetal acceleration, we will use the formula listed below:

a_{c }= v^{2}/ r

Putting values in the formula:

a_{c}= (25 m/s)^{2}/ 15 m = (625 m^{2}/s^{2}) / 15 m = 41.66 m/s^{2}