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.
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Reference