A uniform disc of mass M and radius R is smoothly pivoted at 'O'. A light inextensible strings wrapped over the disc hangs a particle of mass m. If the system is released from rest, assuming string does not slide, what will be the angular speed of the disc as a function of time.

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G1 Physics · Accepted Answer

For the hanging mass, mg-T=ma with a=αR. For the disc, TR=Iα=(MR²/2)α. Solving gives α=2mg/[(M+2m)R], hence ω=αt=2mgt/[(M+2m)R]. Hence A. Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives 2mgt/[(M+2m)R]..