Two disks are mounted (like a merry-go-round) on low-friction bearings on the sa

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 4.44 kg.m^2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 315 rev/min. The second disk, with rotational inertia 6.55 kg-m^2 about its central axis, is set spinning counterclockwise at 984 rev/min. They then couple together. (a) what is their angular speed after coupling? If instead the second disk is set spinning clockwise at 984 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together? (a) Number Units (b) Number Units (c) Click if you would like to show work for this question:

Explanation / Answer

Apply conservation of angular momentum

I1 w1 + I2 w2 = ( I1 + I2) w

w = I1 w1 + I2 w2/( I1 + I2)

=4.44(315) + 6.55(984)/4.44+6.55

=713.72 rev/min

(b)

in this case

w = I1 w1 + I2 w2/( I1 + I2)

=4.44(315) + 6.55(-984)/4.44+6.55

=-459.19 rev/min

(c)

The minus sign indicates that w is clockwise, that is, in the direction of the second
disk’s initial angular velocity

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