A uniform solid disk, with a mass of 2.0 kg and 20 cm in diameter, is rotating about an axis through its center at 200 rpm. A circular hoop, 20.0 cm in diameter with a mass of 1.0 kg, is dropped straight down onto the rotating disk. Friction between the disk and hoop causes the hoop to accelerate until it rotates with the disk at rest with respect to the disk. Calculate the final angular velocity of the combination.