Chapter 11, Problem 049 Two disks are mounted (like a merry-go-round) on low-fri

Question

Chapter 11, Problem 049 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 2.49 kg.m2 about its central axis, is set spinning counterclackwise (which may be taken as the positive direction) at 108 rev/min. The second disk, with rotational inertia S.23 kg.m2 about its central axis, is set spinning counterclockwise at 797 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 797 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 (b) Number (c) clockwise Units rev/min Units rev/min 2

Explanation / Answer

a) apply conservation of angular momentum

If*wf = I1*w1 + I2*w2

wf = (I1*w1 + I2*w2)/If

= (2.49*108 + 5.23*(797))/(2.49 + 5.23)

= 575 rev/min

b) apply conservation of angular momentum

If*wf = I1*w1 + I2*w2

wf = (I1*w1 + I2*w2)/If

= (2.49*108 + 5.23*(-797))/(2.49 + 5.23)

= -505 rev/min

c) clockwise

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