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:

Where, $\omega$ is the angular velocity and t is the time taken.

Thus the angular acceleration $\alpha$ is given by

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

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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?

** Solution: **

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/s^{2}.

**Question 2: **A wheel of a bicycle has an angular acceleration of 10 rad/s^{2} in a second. Find the angular velocity?

** Solution: **

Given: Angular acceleration $\alpha$ = 10 rad/s^{2},

Time taken t = 1 s,

Angular acceleration is given by $\alpha$ = $\frac{d \omega}{dt}$

Angular velocity d $\omega$ = $\alpha$ dt = 10 rad/s^{2 }$\times$ 1s
= 10 rad/s.

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/s

Given: Angular acceleration $\alpha$ = 10 rad/s

Time taken t = 1 s,

Angular acceleration is given by $\alpha$ = $\frac{d \omega}{dt}$

Angular velocity d $\omega$ = $\alpha$ dt = 10 rad/s