In the figure the lower disk, of mass 460 g and radius 3.8 cm , is rotating at 1

Question

In the figure the lower disk, of mass 460 g and radius 3.8 cm , is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 280 g and radius 2.3 cm , is initially not rotating. It drops freely down onto the lower disk, and frictional forces bring the two disks to a common rotational speed

https://session.masteringphysics.com/problemAsset/2096209/1/RW-11-51.jpg

1. Find the common speed.

(in rpm)

2. Find the fraction of the initial kinetic energy lost to friction.

(in %)

Explanation / Answer

here angular momentum is conserve

Li = Lf

I1*wi = (I1+I2)*wf

wi = 180 rpm = 18.85 rad/s

I1 = lower disk moment of inertia = MR^2/2= 3.3212 x 10^-4 kg-m^2

I2 = upper disk moment of interia = 7.406 x 10^- 5kg-m^2

wf = 15.4 rad/s

part 2 )

dKE/KEi

KE = 1/2 * I*w^2

KEf = 1/2 * (I1+I2)*wf^2 = 0.048 J

KEi = 1/2 * I1*wi^2 = 0.05894

dKE/KE = 0.1856 = 18.56%

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