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 3.45 kg-m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 229 rev/min. The second disk, with rotational inertia 7.62 kg-m2 about its central axis, is set spinning counterclockwise at 998 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 998 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after (a) Number Units (b) Number| Units

Explanation / Answer

here,

moment of inertia of 1 , I1 = 3.45 kg.m^2 , w1 = 220 rev/min

moment of inertia of 2 , I2 = 7.62 kg.m^2 , w2 = 998 rev/min

a)

let their final angular speeds be w

using conservation of angular momentum

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

3.45 * 220 + 7.62 * 998 = ( 3.45 + 7.62) * w

solving for w

w = 755.5 rev/min counterclockwise

b)

let their final angular speeds be w

using conservation of angular momentum

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

3.45 * 220 - 7.62 * 998 = ( 3.45 + 7.62) * w

solving for w

w = - 618 rev/min

the magnitude of angular speed is 618 rev/min

c)

the direction of couple is CLOCKWISE

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