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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: Where, $\omega$ is the angular velocity and t is the time taken. Angular Velocity $\omega$ is given by Where, $\theta$ is the angle rotated 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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## 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?
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/s2.

Question 2: A wheel of a bicycle has an angular acceleration of 10 rad/s2 in a second. Find the angular velocity?
Solution:

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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