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A uniform disc of mass M and radius R is free to rotate about a axis O passing through its rim. An insect of mass m at point A such that the line OA is the diameter of the disc as shown in figure. The insect describes a complete circle relative to disc and return to starting point A. Calculate the angle moved by the disc relative to ground.
Asked by dasherbro123 | 16 Apr, 2020, 07:49: PM
Let ωD be the angular velocity of disc and ωi be the angular velocity of insect as shown in figure.

In absence of external torque, angular momentum is conserved.

Hence , ID ωD = Ii ωi  ......................(1)

where ID is moment of inertia of disc about an axis perpendicular to its plane and passing through O.

We have, ID = (1/2)MR2 + MR2 = (3/2)MR2

When the insect moving along the rim of disc and coming to same starting point after time T,
let θ be the angular displacement of disc.

Then angular displacement of insect (2π - θ )

Hence eqn.(1) is rewritten as

From above equation, we get
Answered by Thiyagarajan K | 16 Apr, 2020, 11:00: PM

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