# Angular Velocity Definition

In physics, angular velocity is the rate at which an object rotates and changes its angular velocity over a specific period of time. In mathematical form, an angular velocity is defined as the rate of change of angular displacement of an object at a given period of time. The angular velocity is a vector quantity having both direction and magnitude. Whereas its track can be indicated using the right-hand rule, at which the plane of rotation is vertical to the direction of an object. The SI unit used to represent the angular velocity is radians per second. At the same time, the symbol used for Angular velocity is omega (ω, sometimes Ω).

## Formula of Angular Velocity

The formula used to find the angular velocity is listed below:

$\omega = \frac{{d\theta }}{{dt}}$

Where,

dθ = Change in angular displacement

dt = Change in time

Note:

If you want to calculate angular velocity, you can use our Angular Velocity Calculator.

### Example

For a more precise understanding of the concept, let us solve an example below:

Suppose a car moving in a circular path has an angular displacement of 6.28 radians, whereas the total time taken by a car to complete the first track is 120 seconds, find out the angular velocity at which the car is rotating in a circular path.

Given data

dθ = Change in angular displacement = 6.28 rad
dt = Change in time = 120 sec

To Find

Angular velocity =?

Solution

To find out the angular velocity, we will use the formula listed below:

$\omega = \frac{{d\theta }}{{dt}}$

Putting values in the formula:

ω = 6.28/120 = 0.052 rad/sec