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Question

A rigid body rotates about a fixed axis with a variable angular velocity equal to an abt at time t time where a and b are constants. The angle through which it rotates before it comes to stop is:


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Solution

Given data

  1. The angular velocity of the body is ω=a-bt

Angular velocity

  1. Angular velocity is the time rate of change in the angular displacement of a body.
  2. The angular velocity of a body is defined by the form, ω=dθdt, where θ is the angular displacement of the body.

Finding the angular displacement

As we know, angular velocity is ω=dθdt

So,

dθ=ωdtordθ=a-btdtorθ=a-btdt=at-bt22orθ=at-bt22..........(1)

But when the body stops rotating, its angular velocity is zero.

So,

ω=abt=0ort=ab.................(2)

From equations 1 and 2 we get,

θ=aab-b2a2b2=a22borθ=a22b.

Therefore, the angle through which it rotates before it comes to stop is θ=a22b.


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