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Question

A disc of mass m, radius r wrapped over by a light and inextensible string is pulled by force F at the free end of the string. If it moves on a smooth horizontal surface, find linear and angular acceleration of the disc.

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Solution


The force translates the C.M of the disc with an acceleration
a given as

F=maa=Fm

The force F develops a torque τ about O; consequently the disc rotates with an angular acceleration α about an axis passing through O, given as τ=l0 α
τ=FR & I0=12mR2
α=τI0=FR(1/2)mR2=2FmR
1032987_1015200_ans_f3aad1d7b79e4bb1a3088eccc1b15dc7.png

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