# Formula For Centripetal Acceleration

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Centripetal acceleration is the acceleration acting on an object moving on a circular path with a certain velocity. An object in circular motion constantly experiences a force pulling it towards the center of the circular path. This force is known as the centripetal force and the centripetal acceleration is responsible for this ‘center-seeking’ force on the object. Therefore the direction of the centripetal acceleration is towards the center of the circle and its formula is given as the square of velocity over the radius of the circular path.

Example 1: What is the centripetal acceleration acting on an object travelling on a circular path of radius 8m and velocity of 12m/sec?

The formula for centripetal acceleration is given as: Centripetal acceleration, ac = v2/ r

Here in the above formula, v = velocity of the object = 12m/sec

r = radius of the circular path = 8m

Therefore we get centripetal acceleration, ac = v2/ r ==> ac = (12)2/ (8)

This gives: ac = 144/8 = 18m/sec2
Hence the centripetal acceleration on the object, ac = 18m/sec2

Example 2: What is the centripetal acceleration acting on an object travelling on a circular path of radius 5m and velocity of 6m/sec?

The formula for centripetal acceleration is given as: Centripetal acceleration, ac = v2/ r

Here in the above formula, v = velocity of the object = 6m/sec

r = radius of the circular path = 5m

Therefore we get centripetal acceleration, ac = v2/ r ==> ac = (6)2/ (5)
This gives: ac = 36/5 = 7.2m/sec2
Hence the centripetal acceleration on the object, ac = 7.2m/sec2