A uniform disk has a mass of 4.9 kg and a radius of 0.53 m. The disk is mounted

Question

A uniform disk has a mass of 4.9 kg and a radius of 0.53 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 50 rpm. A hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. The final angular momentum of the system is closest to:

a. 7.2 kg · m2/s
b. 3.6 kg · m2/s
c. 5.2 kg · m2/s
d. 4.4 kg · m2/s
e. 6.2 kg · m2/s

Explanation / Answer

initial angular velocity i = 50 rpm moment of inertia of the disk = (1/2) MR2 moment of inertia of the hollow cylinder = MR2 from law of conservation of angular momentum ,           I1i = I'1f + I'2f          {(1/2) MR2}i = {(1/2) MR2}f + {MR2}f          (1/2) i = {(1/2)+ 1}f final angular velocity is              f = i/3                   = 50 rpm / 3                   = 16.667 rpm                   = (16.667)(2 / 60) rad/s                   = 1.74 rad/s so , final angular momentum of the system is            L = (I + I')f               = {(1/2) MR2 + MR2}f               = (3/2)MR2f               = (3/2)(4.9 kg)(0.53 m)2(1.74 rad/s)               = 3.6 kg-m2 /s answer : option 'b' is correct answer                    

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