The uniform cylinder A, of mass m and radius r, has an angular velocity 0 when it

Question:

The uniform cylinder A, of mass m and radius r, has an angular velocity ω0 when it is brought into contact with an identical cylinder B which is at rest. The coefficient of kinetic friction at the contact point D is μk. After a period of slipping, the cylinders attain constant angular velocities of equal magnitude and opposite direction at the same time. Knowing that the final kinetic energy of the system is one-half the initial kinetic energy of cylinder A, derive expressions for the number of revolutions executed by each cylinder before it attains a constant angular velocity.