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 2.98 kg-m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 299 rev/min. The second disk, with rotational inertia 6.41 kg-m about its central axis, is set spinning counterclockwise at 762 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 762 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

Explanation / Answer

(A) I1 = 2.98 kg m^2

w1 = 299 rev/min

I2 = 6.41 kg m^2

w2 = 762 rev/min

Applying angular momentum conservation,

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

wf= 615 rev/min

(b) w1 = +299 rev/min

w2 = - 762 rev/min

(2.98 x 299) + (6.41 x -762) = (2.98 + 6.41)wf

wf = - 428.5 rev/min

(C) direction - clockwise

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