## 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** = 360^{0}

and **θ** = 360^{0} is the same thing as 2*π* radians

[where *π* =180^{0} and 2 x 180^{0} = 360^{0}]

Therefore,

The angle made in 8 complete revolutions = 8 x 2*π* radians = 16*π* 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 = 16*π* radians/4 seconds

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

Therefore, the angular velocity is 4*π* 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.

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**Reference**