Two disks are mounted on low-friction bearings on the same axle and can be broug

Question

Two disks are mounted 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 a rotational inertia of 2.508 kg-m^2 about its central axis, is initially spinning at a rate of 621 rpm. The second disk , with a rotational inertia of 4.092 kg-m^2 about its central axis, is initially spinning at a rate of 684 rpm in the same direction as the first one. They then couple together a) What is their angular speed after coupling? b) If the second disk is initially spinning opposite to the first one , what is the angular speed after coupling ?

Explanation / Answer

Data: Moment of inertia of first disk, I1 = 2.508 kg.m^2 Moment of inertia of second disk, I2 = 4.092 kg.m^2 Solution: (a) Initial angular velocity of first disk, 1 = 621 rpm Initial angular velocity of second disk, 2 = 684 rpm Final angular velocity after coupling, = ? According to the law of conservation of angular momentum,               ( I1 + I2 ) = I1 1 + I2 2 ( 2.508 + 4.092 ) * = 2.508 * 621 + 4.092 * 684                          6.6 = 1557.468 + 2798.928                          6.6 = 4356.396                                = 660.1 rpm Ans: Angular velocity after coupling, = 660.1 rpm (b) Initial angular velocity of first disk, 1 = 621 rpm Initial angular velocity of second disk, 2 = - 684 rpm Final angular velocity after coupling, = ? According to the law of conservation of angular momentum,               ( I1 + I2 ) = I1 1 + I2 2 ( 2.508 + 4.092 ) * = 2.508 * 621 - 4.092 * 684                          6.6 = 1557.468 - 2798.928                          6.6 = - 1241.46                                = - 188.1 rpm Ans: Angular velocity after coupling, = - 188.1 rpm Note: Here, '-ve' sign indicates that its direction is opposite to that           of first disk. Initial angular velocity of first disk, 1 = 621 rpm Initial angular velocity of second disk, 2 = - 684 rpm Final angular velocity after coupling, = ? According to the law of conservation of angular momentum,               ( I1 + I2 ) = I1 1 + I2 2 ( 2.508 + 4.092 ) * = 2.508 * 621 - 4.092 * 684                          6.6 = 1557.468 - 2798.928                          6.6 = - 1241.46                                = - 188.1 rpm Ans: Angular velocity after coupling, = - 188.1 rpm Note: Here, '-ve' sign indicates that its direction is opposite to that           of first disk.

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