A uniform disk has a mass of 4.6 kg and a radius of 0.2 m. The disk is mounted o

Question

A uniform disk has a mass of 4.6 kg and a radius of 0.2 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 20 rpm. A thin-walled 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. What is the final angular momentum of the system?

Explanation / Answer

initial angular velocity w1= 30 rpm

moment of inertia of the disk = (1/2) MR^2

moment of inertia of the hollow cylinder = MR^2

from law of conservation of angular momentum ,

I1*w1 = I'1*w2 + I'2*w2

(1/2) MR^2*w1= (1/2) MR^2*w2+ MR^2*w2

(1/2) w1= [(1/2)+ 1]*w2

final angular velocity w2 = w1/3

w2 = 30/3 = 10 rpm

w2 = 10 rpm = 10*2pi/60 = 1.047 rad/s

final angular momentum L = (I + I')*w2

L = [(1/2) MR^2 + MR^2]*w2

L = (3/2)MR^2*w2

L = (3/2)*3.7 * 0.4^2 * 1.047

L = 0.93 Kgm^2/s

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