Question

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 2.11 kg·m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 372 rev/min. The second disk, with rotational inertia 8.41 kg·m2 about its central axis, is set spinning counterclockwise at 631 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 631 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?

Answer 1

Since no external torque is acting on the system you can use the conservation of angular momentum. I derived the final angular speed below and shown my work on how I did it. It’s now just a matter of plugging in the numbers and using correct placement of negative sign for direction of angular velocity. L in the picture stands for angular momentum. Hope it helps