Angular Displacement

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Angular displacement is the angle at the centre of circular path by which the object rotates. It simply means the angle created by the circular movement of the object at the circumference of the circular path.

Consider the object moves from A to B in circular path in t time which makes θ angle at the centre O, This angle θ is called angular displacement.
If the distance between A and B is “d” then,
                                      d = rθ
Thus,                             θ = d/r
Also,                              θ = ωt
Where, r = radius of circle.
          ω = angular velocity
          t = time taken
Example:  A body is moving in a circular path with an angular speed of 63 rad/Sec. Calculate its angular displacement at time t = 7 s?
Solution: Given that,
                   Angular speed, ω = 63 rad/sec
                   Time taken, t = 7 sec
We have equation for angular displacement,
                             θ = ωt = 63 x 7 = 441 radians.
Example2: A motor bike is moving in circular track covers the whole track of distance 45m having radius of 9m from the center. Find its angular displacement.

Solution: Given that, Displacement, d = 45 m

Radius of circle, r = 9 m

So that,                θ = d/r

                                 = 45/9 = 5 radians.

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