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Angular velocity is the rate of change of angular displacement with time.
If a body moving in a circular path turns through an angle ${\theta}$ radians in time ‘t’, we define angular velocity omega (${\omega}$), as the rate of change of the angle ${\theta}$ with time. ${\omega}$= ${\theta}$ / t, unit for angular velocity is radians per second (rads-1). Since the radian measure is a ratio we can write it as second-1 (s-1). We can establish the relationship between angular velocity ‘${\omega}$’ and linear velocity ‘v’, from the relation, ${\theta}$ = arc / radius, arc = radius × ${\theta}$. Dividing the expression by ‘t’, then arc / t = radius, but arc / t = v (angular velocity). So ‘v’ = radius × ${\omega}$. This expression gives us the relationship between angular and linear velocity.
johnmulu answered the question on February 18, 2017 at 09:22
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