When an object is moving on a circular path, it constantly changes its direction of motion and hence forms an angle at the center. Due to this reason, in circular motion the object has angular distance and angular speed along with its linear speed. This angular speed is the angular distance (considered in terms of rotations or revolutions) over a period of time. Angular speed formula is also related to linear speed and is given as linear speed over the radius of the circular path.
Example 1: An object takes a time period of 10secs to make 1 complete rotation on a circular path. What is angular speed of the object?
Angular speed is represented by the letter, ‘ω’.
The formula is given by: Angular speed, ω = θ/ t
Here in the above formula, ‘θ’ = angular distance in radians = 1 rotation = 2π radians
‘t’ = time period = 10secs
Therefore, angular speed, ω = 2π/ 10 ==> ω = (π/ 5) = 0.628 rad/secs
Hence, the angular speed of the given object, ω = 0.628 rad/secs
Example 2: A car travels on a circular path of radius 6m with a linear speed of 24m/sec. What is the
angular speed of the car?
The formula is given by: Angular speed, ω = v/ r
Here in the above formula, ‘v’ = linear speed of the car = 24m/secs
‘r’ = radius of the circular path = 6m
Therefore, angular speed, ω = v/ r ==> ω = 24/ 6 = 4 rad/secs
Hence, the angular speed of the given car, ω = 4 rad/secs.