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Two horizontal discs rotate freely about...

Two horizontal discs rotate freely about a vertical axis passing through their centres. The moments of inertia of the discs relative to this axis are equal to `I_1` and `I_2`, and the angular velocities to `omega_1` and `omega_2`. When the upper disc fell on the lower one, both discs began rotating, after some time, as a single whole (due to friction). Find:
(a) teh steady-state angular rotation velocity of the discs,
(b) the work performed by the friction forces in this process.

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