Angular Displacement Formula

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Angular displacement is the angle in degree or radian created by the circular motion of the object at the circumference of the circular path.

If an object covers d distance at the arc of the circle, it creates θ angle at its center and it relates to the formula:

                                      d = rθ

Here, r = radius of the circle.

                   Also,    θ = ωt        

Where,  ω = angular velocity

                t = time taken.

Example: After 12.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +2.45 rad/s. During this time, the wheel has an angular acceleration of -7.5 rad/s2. Determine the angular displacement of the wheel.

Solution: Given that,

Angular velocity = 2.45 rad/s

 Angular acceleration = 7.5 rad/s^2

  Time = 12 sec

As we know that, in linear motion

  d = vt + ½ at^2

We can use the same equation in circular motion,

   θ = ωt + ½ αt^2

      = (2.45)(12) + ½ (7.5)(12)^2

      = 569.4 radians

Example: A car is moving in circular track covers the whole track of distance 25m having radius of 5m from the center. Find its angular displacement.

Solution: We have given,

Displacement, d = 25 m

 Radius of the circle, r = 5 m

So that,     θ = d/r

                   = 25/5 = 5 radians.

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