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Question

A rigid body is rotating about a vertical axis at n rotations per minute. If the axis slowly becomes horizontal in t seconds and the body keeps on rotating at n rotations per minute then the torque acting on the body will be, if the moment of inertia of the body about axis of rotation is I.

A
Zero
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B
2πnI60t
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C
22πnI60t
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D
4πnI60t
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Solution

The correct option is B 22πnI60t
Given that the axis of rotation is slowly changed to vertical to horizontal.
So, we can say that torque magnitude didn't change during the whole movement.
angular velocity,
ω=n×2π60rads1
Since , torque=dLdt{since ,l=Iω}
torque=I×ΔωΔt
|ω|=|ω|
Δω=ω2+ω2=2ω since ωω
by substituting,
Torque acting on the body=22πnI60t

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