Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 49

49 Two disks are mounted (like a merry-go-round) on low friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia \(3.30 \text{ kg}\cdot\text{m}^2\) about its central axis, is set spinning counterclockwise at \(450 \text{ rev/min}\). The second disk, with rotational inertia \(6.60 \text{ kg}\cdot\text{m}^2\) about its central axis, is set spinning counterclockwise at \(900 \text{ rev/min}\). They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at \(900 \text{ rev/min}\), what are their (b) angular speed and (c) direction of rotation after they couple together?