No slippage

Classical Mechanics Level pending

A spool of mass M M is resting on a horizontal surface. The spool has moment of inertia M G c 2 MG^{2}_{c} about its axis of symmetry. Now, the spool is subjected to a rightward horizontal force of magnitude F , F, applied at a distance of r r above the axis. Find the leftward frictional force f , f, given that there is no slippage between the spool and the surface.

f = F ( G c 2 + r R ) ( G c 2 − R 2 ) f = \frac{F(G^{2}_{c}+rR)}{(G^{2}_{c}-R^{2})} f = F ( G c 2 − r R ) ( G c 2 + R 2 ) f = \frac{F(G^{2}_{c}-rR)}{(G^{2}_{c}+R^{2})} f = F ( G c 2 + r R ) ( G c 2 + R 2 ) f = \frac{F(G^{2}_{c}+rR)}{(G^{2}_{c}+R^{2})} f = F ( G c 2 − r R ) ( G c 2 − R 2 ) f = \frac{F(G^{2}_{c}-rR)}{(G^{2}_{c}-R^{2})}

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Srinivasa Satti by Srinivasa Satti

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