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# Angular Displacement Formula

The angular displacement is the angle through which a body rotates in circular path. It is denoted by $\theta$ and expressed in radians or degrees.
Angular Displacement Formula

Angular displacement formula is used to find the angular displacement $\theta$ made by the body in time t.
Angular displacement formula in terms of angular velocity is given by

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

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## Angular Displacement Problems

Here are some problems given on angular displacement based on the above formula.

### Solved Examples

Question 1: A motor bike is moving in circular track covers the whole track of distance 50m having radius of 4m from the center. Find its angular displacement.
Solution:

Given: Linear displacement S = 50 m,
Radius of circular path r = 4 m,
The angular displacement is given by
$\theta$ = $\frac{S}{r}$
= $\frac{50}{4}$

Question 2: A body is moving in a circular path with a angular speed of 59 rad/sec. Calculate its angular displacement at time t = 5 s?
Solution:

given: Angular speed $\omega$ = 59 rad/sec,
Time t = 5 s
The angular displacement is given by
$\theta$ = $\omega$ t
= 59 $\times$ 5