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).
Table of Contents
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
