Question

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.

Answer 1

(a) From the law of conservation of angular momentum of the system relative to vertical axis z, it follows that:

Not that for ω > 0, the corresponding vector with the poitive direction to the z axis, and vice versa. As both discs rotates about the same vertical axis z, thus in vector form.