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 angle made in 8 complete revolutions = 8 x 2π radians = 16π radians

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

Radius, r = 4 m

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.

You may also like to read:

How to Calculate Centripetal Force

Reference

Wikipedia