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 I1 and I2, and the angular velocities to ω1 and ω2. 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) The steady-state angular rotation velocity of the discs;
(b) The work performed by the friction forces in this process.