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 1.73 kg·m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 317 rev/min. The second disk, with rotational inertia 7.41 kg·m2 about its central axis, is set spinning counterclockwise at 621 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 621 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?

Explanation / Answer

(a)

initial angular of the system Li = I1*w1 + I2*w2

after coupling final angular momentum Lf = (I1+I2)*w

from conservation angular momentum Lf = Li

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

(1.73 + 7.41)*w = (1.73*317) + (7.41*621)

angular velocity w = 563.4 rev/min

---------------

(b)

initial angular of the system Li = I1*w1 - I2*w2

after coupling final angular momentum Lf = (I1+I2)*w

from conservation angular momentum Lf = Li

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

(1.73 + 7.41)*w = (1.73*317) - (7.41*621)

angular velocity w = -443.5 rev/min

angular velocity = 443.5 rev/min

(c)

clockwise direction

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