Today we are going to discuss Centripetal Acceleration which is also known as Radial Acceleration. The term centripetal is termed by Sir Isaac Newton and the meaning of centripetal is "centre seeking".

The word centripetal is the combination of two Latin words 'Centrum' (which means 'centre') and 'Petera' (which means 'to seek').

We know that the rate of change of velocity with time is acceleration. While rotation of an object in a circular path when the acceleration is perpendicular to the direction of the velocity then the phenomenon can be called as centripetal acceleration or radial acceleration.

## Centripetal Acceleration Definition

Centripetal acceleration can be defined as the acceleration acting on the object undergoing uniform circular motion.

Or

Centripetal acceleration is the rate of change in velocity of an object that is associated with the change in direction of the velocity.

Or

The linear acceleration that causes the tangent of velocity to change direction is centripetal acceleration.

Centripetal acceleration always act on the motion object along with the radius towards the centre of the circular path or we can say it is always directed inward.

• Centripetal acceleration is always perpendicular to the velocity.
• centripetal acceleration always points towards the centre of the curve.
• Centripetal acceleration is always directed inward.

## Centripetal Acceleration Unit

The centripetal acceleration is denoted by ac and the SI unit of centripetal acceleration is metre per second squared (m/s2).

Centripetal acceleration.             m/s2

## Centripetal Acceleration Formula

The formula of centripetal acceleration can be written as the square velocity divided by the radius of the circular path. The formula is as follows,

ac = v2/r

Where,
• ac is centripetal acceleration
• v is velocity (linear speed)
• r is the radius of the circle

Now, we are going to connect the centripetal acceleration with the magnitude of angular velocity which is denoted by Omega (w). Let's see the formula derivation.

We know that formula of velocity is,

v = rw

Now, put the formula for centripetal acceleration

ac = v2 / r
ac = (rw)2 / r
ac = r w2

Where,
• ac is the centripetal acceleration
• r is the radius of the motion object
• w velocity of the body