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Angular Acceleration Formula

Angular Acceleration is the rate of change of angular Velocity with respect to time. It is a vector quantity. It is denoted by $\alpha$. The Angular Acceleration Formula is given by:
Angular Acceleration Formula

Where, $\omega$ is the angular velocity and t is the time taken.
Formula for Angular Acceleration
Angular Velocity $\omega$ is given by
Angular Acceleration Formula
Where, $\theta$ is the angle rotated and t is the time taken.

Thus the angular acceleration $\alpha$ is given by
Formula for Angular Acceleration

These formulas are helpful in solving problems based on angular acceleration.

Related Calculators
Angular Acceleration Calculator Acceleration Formula Calculator
Angular Momentum Calculator Angular Speed Calculator

Angular acceleration Problems

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Below are given problems on angular acceleration which helps to use these formulas.

Solved Examples

Question 1: The angular velocity is changing at the rate of 30 rad/s for 5 s. Calculate the angular acceleration?
Given: Angular velocity d $\omega$ = 30 rad/s,
         Time taken t = 5s,
         Angular acceleration is given by $\alpha$ = $\frac{d \omega}{dt}$
                                                                           = $\frac{30}{5}$
                                                                           = 6 rad/s2.

Question 2: A wheel of a bicycle has an angular acceleration of 10 rad/s2 in a second. Find the angular velocity?
Given: Angular acceleration $\alpha$ = 10 rad/s2,
          Time taken t = 1 s,
Angular acceleration is given by $\alpha$ = $\frac{d \omega}{dt}$
Angular velocity d $\omega$ = $\alpha$ dt = 10 rad/s2 $\times$ 1s = 10 rad/s.

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