A cylinder with moment of inertia I1 rotates about a vertical, frictionless axle with angular speed i. A second cylinder, this one having moment of

A cylinder with moment of inertia I1 rotates about a vertical, frictionless axle with angular speed ώi. A second cylinder, this one having moment of inertia I2 and initially not rotating, drops onto the first cylinder (Fig. P11.28). Because of friction between the surfaces, the two eventually reach the same angular speed ώf.
(a) Calculate ώf.
(b) Show that the kinetic energy of the system decreases in this interaction, and calculate the ratio of the final to the initial rotational energy.

a, Before After Figure P11.28