Angular Velocity

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Angular velocity is the rate of change of angular displacement with respect to time. Similar to the linear motion, where velocity is the rate of change of displacement, in a circular motion it is known as angular velocity.
                   ω = dθ/dt
 also,           ω = θ/t

Where, dθ = change in angular displacement

 θ = angular displacement

 dt = change in time

   t = time taken

The relation between angular and linear velocity is:

 ω = v/r      
 
Where, v = linear velocity

And   r = radius of the circle

 
Example: A circular wheel of 1.25 m radius is moving with a speed of 25 m/s. Find the angular velocity?

Solution: We have given that,

Linear speed, v = 25 m/s

          Radius, r = 1.25 m

No, we have the equation for angular velocity,

          Angular velocity, ω = v/r = 25/1.25 = 20 rad/sec

 
Example: Find the angular velocity of a second hand of a clock?




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