Two disks are mounted like a merrygoround on lowfriction bea

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 3.36 kg·m² about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 455 rev/min. The second disk, with rotational inertia 8.91 kg·m² about its central axis, is set spinning counterclockwise at 716 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 716 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?

Solution

w_f = I₁ w₁ + I₂ w₂ / (I₁ + I₂)

= (3.36*455 + 8.91*716) / (3.36 + 8.91)

= 644.53 rev/min

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w_f = I₁ w₁ + I₂ w₂ / (I₁ + I₂)

= (3.36*455 + 8.91*-716) / (3.36 + 8.91)

= -395.33 rev/min