Angular velocity of an object is given as the amount of rotation around a central point per unit of time. The amount of ration may be a expression of degrees or radians
Revolution In degrees / radians
To degrees: revolutions * 360 To radians: revolutions * 2pi Does this make sense?
Example
A fan makes 60 rotations in 5 seconds. what is its angular velocity?
Solution
12 rotations a second. To radians, a rotation is 2pi. so 12*2pi = 24pi