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 4.05 kg.m^2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 288 rev/min. The second disk, with rotational inertia 6.65 kg.m^2 about its central axis, is set spinning counterclockwise at 982 rev/min. They then couple together, (a) What is their angular speed after coupling If instead the second disk is set spinning clockwise at 982 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together Number Units Number Units

Explanation / Answer

Here ,

moment of inertia , I1 = 4.05 Kg.m^2

initial angular speed , wi = 288 rev/min

w1 = 288 rev/min

moment of inertia of second disk , I2 = 6.65 Kg.m^2

angular speed of disk 2 , w2 = 982 rev/min

a) let the final angular speed is wf

Using conservation of angular momentum

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

4.05 * 288 + 6.65 * 982 = (4.05 + 6.65) * wf

wf = 713.3 rev/min

the final angular speed of the disks after coupling is 713.3 rev/min

b)

for w2 = -982 rev/min

Using conservation of angular momentum

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

4.05 * 288 - 6.65 * 982 = (4.05 + 6.65) * wf

wf = - 501.3 rev/min

the final angular speed after coupling is 501.3 rev/min

c)

the direction of motion after coupling is clockwise

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