Two-cylindrical-hollow-drums-of-radii-R-and-2R-and-of-a-common-height-h-are-rotating-with-angular-velocities-anti-clockwise-and-clockwise-respectively-Their-axes-fixed-are-parallel-and-in

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Question Number 24434 by Tinkutara last updated on 17/Nov/17

$$\mathrm{Two}\mathrm{cylindrical}\mathrm{hollow}\mathrm{drums}\mathrm{of}\mathrm{radii}$$$$R\mathrm{and}2R,\mathrm{and}\mathrm{of}\mathrm{a}\mathrm{common}\mathrm{height}h,$$$$\mathrm{are}\mathrm{rotating}\mathrm{with}\mathrm{angular}\mathrm{velocities}\omega$$$$(\mathrm{anti}-\mathrm{clockwise})\mathrm{and}\omega \left(\mathrm{clockwise}\right),$$$$\mathrm{respectively}.\mathrm{Their}\mathrm{axes},\mathrm{fixed}\mathrm{are}$$$$\mathrm{parallel}\mathrm{and}\mathrm{in}\mathrm{a}\mathrm{horizontal}\mathrm{plane}$$$$\mathrm{separated}\mathrm{by}(3R+\delta ).\mathrm{They}\mathrm{are}\mathrm{now}$$$$\mathrm{brought}\mathrm{in}\mathrm{contact}(\delta \to 0).$$$$\left(\mathrm{a}\right)\mathrm{Show}\mathrm{the}\mathrm{frictional}\mathrm{forces}\mathrm{just}\mathrm{after}$$$$\mathrm{contact}.$$$$\left(\mathrm{b}\right)\mathrm{Identify}\mathrm{forces}\mathrm{and}\mathrm{torques}\mathrm{external}$$$$\mathrm{to}\mathrm{the}\mathrm{system}\mathrm{just}\mathrm{after}\mathrm{contact}.$$$$\left(\mathrm{c}\right)\mathrm{What}\mathrm{would}\mathrm{be}\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{final}$$$$\mathrm{angular}\mathrm{velocities}\mathrm{when}\mathrm{friction}\mathrm{ceases}?$$

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