A uniform disk has a mass of 2.6 kg and a radius of 0.75 m. The disk is mounted

Question

A uniform disk has a mass of 2.6 kg and a radius of 0.75 m. The disk is mounted on frictionless
bearings and is used as a turntable. The turntable is initially rotating at 60 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. The loss of kinetic energy of the system is
closest to:

answer is 9.6 J. HOW DO YOU DO IT?!?!?!?! please show step by step with numbers

Explanation / Answer

moment of inertia of the disk. I1=mr^2/2. = 0.73 moment of inertia of the cylinder. I2=mr^2. =1.46 conservation of angular momentum. so we have I1*w=(I1+I2)*w'. where w be initial angular velocity. w=60*2pi/60=2pi(rad/s) so w'=2pi*I1/(I1+I2)=2pi/3 ----- energy lost. w^2*I1/2-w'^2*(I1+I2)/2=9.6(J)

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