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# How to Calculate Angular Velocity in Radians per Second

## Example

Here is How to calculate angular velocity in radians per second:

### Example 1

A stone whirled at the end of a rope 50 centimeters long, makes 8 complete revolutions in 4 seconds. Calculate the angular velocity in radians per second.

Solution

Data:

One complete revolution makes an angle θ = 3600

and θ = 3600 is the same thing as 2π radians

[where π =1800 and 2 x 1800 = 3600]

Therefore,

The time for 8 complete revolutions = 4 seconds

we can now calculate the angular velocity by applying the formula that says

Angular velocity,  ω = θ/t

By substituting our data into the above formula, we will get

Angular velocity,  ω = θ/t = 16π radians/4 seconds

We will now have ω = 4 π radians/seconds or 4π rad/s

Therefore, the angular velocity is 4π radians per second.

### Example 2

An object is moving along a circular path with a radius of 4 meters and a linear velocity of 16 meters per second. Determine the angular velocity of the object in radians per second.

Solution

Data:

Speed, v = 16 m/s

angular velocity =?

and the formula for calculating the angular velocity is

Angular velocity,  ω = v/r

We can now substitute our data into the above formula

Angular velocity,  ω = 16/4 = 4 radians per second or 4 rads-1

Therefore, the angular velocity of the object is 4 radians per second.

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Reference

Wikipedia