Angular acceleration is the measure by which the angular velocity of an object changes over time. It describes how fast an object turns. It is represented by the symbol α. In  simpler words, if you envision any rotating body, the angular acceleration will let you know how quickly it is speeding up or slowing the rotation.

Angular acceleration is represented by α with the units of rad/s2 or radians per second square.

Formula

Angular acceleration is defined as given below,

And also in terms of double differentiation of angular displacement, as represented below,

Derivation:

Angular acceleration is the rate of change of angular velocity with respect to time, or we can write it as,

Here, α is the angular acceleration that is to be calculated, in terms of rad/s2, ω is the angular velocity given in terms of rad/s and t is the time taken expressed in terms of seconds.

The Angular velocity as we know can be expressed as given below.

Here, ω is the angular velocity in terms of rad/s, v is the linear velocity and r is the radius of the path taken.

Angular Velocity can also be expressed as the change in angular displacement with respect to time, as given below.

Where θ is the angular rotation of the object and t is the total time taken.

By using the above formula, we can write angular acceleration α as

Solved Problems

Problem 1: An ant is sitting at the edge of a rotating circular disc. Its angular velocity changes at the rate of 60 rad/s for 10 seconds. Calculate its angular acceleration during this time?

Solution:

Given: The change in angular velocity is dω = 60 rad/s. 

           The time taken for this change to occur is equal to t = 10s.

Making use of the angular acceleration formula and substituting the above values, we get,

Problem 2:The rear wheel of a motorcycle undergoes an angular acceleration of 20 rad/s2 in a second. What can be told about its angular velocity?

Answer:

Given: The angular acceleration of the wheel is equal to α = 10

            Time taken t = 1 s,

According to the formula for angular acceleration,

Putting the values in it, we get,

Angular velocity d is,

                  dω = αdt

                   dω =20×1 

      = 20 rad/s

 

 

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