# Angular acceleration vs Centripetal acceleration – Difference

The primary distinction between angular acceleration vs centripetal acceleration is that angular acceleration is the rate of change of angular velocity with respect to time, whereas centripetal acceleration is the acceleration found in an object rotating in a circular path caused due to the constant change in the direction of the motion.

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## Angular acceleration:

Angular acceleration is the rate of change of angular speed with respect to time. It is denoted by the symbol ‘α’ and measured in terms of rad/s².
The term angular acceleration is analogous to linear acceleration in linear motion.

It is given by,

α = \mathbf{\frac{d\omega}{dt}}

The above figure indicates the angular velocities of the object at two different positions within a time interval (t_{12}) of 5 seconds.

Thus the angular acceleration of the object while moving from position 1 to 2 is given by,

α = \frac{\omega_{2}-\omega_{1}}{t_{12}}

α = \frac{5-4}{5}

## Centripetal acceleration:

Centripetal acceleration (Radial acceleration) causes due the constantly changing direction of the object undergoing circular motion and it is always directed towards the center of rotation.

It is denoted by the symbol a_{c} and measured in terms of the m/s².

The above figure shows the object moving in the circular path with a tangential velocity of v_{t}.
In this case, the centripetal acceleration acting on the object is given by,

a_{c} = \frac{v_{t}^{2}}{r}

The above equation indicates that the centripetal acceleration in the object is directly proportional to the square of the tangential velocity and inversely proportional to the radius of rotation of the object.

## FAQ:

Does angular acceleration affect centripetal acceleration?

No, the angular acceleration never affects the centripetal acceleration.

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