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 3.30 kg- m2 about its central axis, is set spinning counterclockwise at rotational inertia 660kg m* about its central axis, is set spinning counterclockwise at 900 revmn. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 900 rewmin, what are their (b) angular speed and (c) direction of rotation after they couple together? 4 The second disk, with

Explanation / Answer

(a)

From law of conservation of angular momentum,

l1w1 + l2w2 = (l1 + l2) * w

where w = angular speed of disks after coupling

put the values,

3.3*450 + 6.6*900 = (3.3 + 6.6) * w

w = 750 rev / min

(b)

if second disk is spinning clockwise,

3.3*450 + 6.6*(-900) = (3.3 + 6.6) * w

w = -450 rev / min

(c)

Direction of rotation is clockwise after they couple together.

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