We all know what acceleration is and its definition. Acceleration is defined as the rate of change of velocity with respect of time. Same way, the change of angular velocity will be called angular acceleration.

angular-acceleration-formula

Angular acceleration is also known as rotational acceleration because it is a quantitative expression of the change in angular velocity of a rotating object per unit time.


Angular Acceleration Definition

Angular acceleration is defined as the rate of change of angular velocity with respect of time.

Angular Acceleration Symbol- The symbol alpha (α) which is a Greek latter is used for representing the angular acceleration of a body.


Angular Acceleration Examples 

These are some great examples of angular acceleration which you see in your daily life. The examples are,
  1. When you turn on the fan it starts spinning from the rest mode and after 10 seconds it starts spinning at 5 radians per second just because of angular acceleration.
  2. We all know about Ferris wheel and when it starts the speed increases in seconds from the position of rest. It produces angular acceleration.
  3. When we start our bikes and accelerate the bike's wheel speed increases within seconds. This situation also produces angular acceleration.

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Types of Angular Acceleration

The angular acceleration can be categorised as two types.
  1. Spin angular acceleration
  2. Orbital angular acceleration
The spin angular acceleration can be defined as the rate of change of spin angular velocity with respect of time. And the rate of change of orbital angular velocity with time is the orbital angular acceleration.


Angular Acceleration Unit

The SI unit of angular acceleration is radians per second squared (rad/s2).


Angular Acceleration                 rad/s2 or rad • s-2


The length and magnitude of the angular acceleration vector is directly proportional to the rate of change of angular velocity.

Angular acceleration is neither a scaler quantity nor a vector quantity as velocity is always changing while the object is moving.

Angular acceleration has three dimensions and due to this it is a pseudovector. The direction of angular acceleration is perpendicular towards the object rotating.

Angular acceleration occurs when the angular velocity changes over time.

It acts in the direction of rotation in a circular motion (not the same as centripetal acceleration)

In this case we must also introduce tangential acceleration (a1) since the tangential velocity is changing.

         - If there is angular acceleration, there will also be tangential acceleration.


Angular Acceleration Formula

As we already know angular acceleration represented by α and mathematically the formula can be expressed as,

Angular acceleration = change is angular velocity / total time taken

= Final angular velocity - initial angular velocity / total time taken

α = wf - wi / ∆t
α = ∆w /∆t

Where,
  • α is angular acceleration
  • ∆w is change in angular velocity
  • ∆t is total time taken

If the angular velocity of an object is rotating at constant speed (uniform angular velocity) then the angular acceleration of the body will be always zero.

If the angular velocity is non-uniform then we can calculate the angular acceleration with the above formula.

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Angular Acceleration Questions with Solution