A horizontal disc rotating freely about a vertical axis

Asked by admin @ 16/08/2021 in Physics viewed by 394 People

A horizontal disc rotating freely about a vertical axis through its centre makes 90 revolutions per minute. A small piece of wax of mass m falls vertically on the disc and sticks to it at a distance r from the the axis. If the numberof revolutions per minute reduce to 60, then the moment of inertia of the disc is ?

Answered by admin @ 16/08/2021

The moment of inertia of the disc is 2mr²

Explanation:

Let I be the moment of inertia of disc
Moment of inertia of wax = mr²
After wax falls the net moment of inertia = I + mr²

Since there is no external torque acting on the system.
So the angular momentum of the system will remain constant.

Iω = ω₁(I + mr²)

I x 90 = 60(I + mr²)

1.5 I = I + mr²

0.5 I = mr²

I = 2mr²

Hence the moment of inertia of the disc is 2mr²

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