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a uniform horizontal circular disc of mass M and radius R can freely rotate about a vertical axle passing through its centre. A particle of mass m is intially placed near the centre of the disc in a smooth grove made along the radius of the disc.An intial angular velocity w 0 is imparted to the disc. find the angular velocity of the disc,when the particle reaches the other end of the grove.

a uniform horizontal circular disc of mass M and radius R can freely rotate about a vertical axle passing through its centre. A particle of mass m is intially placed near the centre of the disc in a smooth grove made along the radius of the disc.An intial angular velocity w0 is imparted to the disc. find the angular velocity of the disc,when the particle reaches the other end of the grove.

Grade:12

2 Answers

Khimraj
3007 Points
7 years ago
As external torque is zero just apply conservation of angular momentum. I1W1 = I2W2. So (MR²/2)w0 = (MR²/2 + mR²)w. So new w = Mw0/(M+2m). Hope it clears. If still u have doubts then please clarify. If u like answer then please approve the answer.
Spandan Mallick
12 Points
5 years ago
Angular Momentum is conserved.
I (initial) × w (initial) = I (final) × w (final)
=>(MR^2/2) (wi) = {(MR^2/2)+(MR^2)} (wf)
=> wf = (Mwi)/(M+2m)
Since no relation is given between M and m, this ill be the answer. If there is any relation between M and m (which I think should be there), put the relation and get the relation.
 
Hope it helps.
Spandan Mallick, JEE Aspirant.

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