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# Angular Velocity Calculator

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To describe the rotational motion, we need a variable that describes how the angular position $\theta$ is changing with time. That variable is the angular velocity, denoted by $\omega$. The angular velocity $\omega$ is a measure of how rapidly the angle $\theta$ is changing with time. If we are interested in the rotational motion over a time, we can define the angular velocity as,
$\omega$ = $\frac{\theta}{t}$
Where,
$\theta$ is the angular displacement,
t is the time taken.

## Steps

Step 1 : Put down the given parameters with their values from the question.

Step 2 : Find out the unknown variable according to the question, by substituting the given values in the the formula.

$\omega$ = $\frac{\theta}{t}$

## Problems

Let us discuss the problems related to angular velocity.

### Solved Examples

Question 1: Calculate the angular velocity of a body, if the angular displacement at 2s is $\frac{3 \pi}{2}$ rad.

Solution:

Given that,

$\theta$ = $\frac{3 \pi}{2}$, t = 2s

Angular velocity of the given body is,

$\omega$ = $\frac{\theta}{t}$

$\omega$ = $\frac{3 \pi}{2\times2}$ = 2.356 rad/s

Question 2: The angular displacement of a body at 3s is 2 $\pi$ rad. Calculate the angular velocity.

Solution:

Given that,

$\theta$ = 2 $\pi$, t = 3s

Angular velocity of the given body is,

$\omega$ = $\frac{\theta}{t}$

$\omega$ = $\frac{2 \pi}{3}$ = 2.094 rad/s