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 Form 4 Physics uniform circular motion online lessons

Definition of an angular velocity

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Answer Text:
Angular velocity
-If a body moving in a circular path turns through an angle θ radians in time ‘t’, we define angular velocity omega (ω), as the rate of change of the
angle θ with time. ω= #θ / 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 ‘ω’ and linear velocity ‘v’, from the relation, θ = #(arc) / (radius)#, arc = radius × θ.
-Dividing the expression by ‘t’, then #(arc) / t# = radius, but #(arc) / t = v (angular velocity). So ‘v’ =radius × ω.
-This expression gives us the relationship between angular and linear velocity.