A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted

ID: 1474506 • Letter: A

Question

A uniform disk has a mass of

3.7

kg and a radius of

0.40

m. The disk is mounted on frictionless

bearings and is used as a turntable. The turntable is initially rotating at

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?

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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