# Physics Question, Help!?

In the figure the lower disk, of mass 450g and radius 3.1 cm , is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 270 g and radius 2.0 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.

A. Find the common speed.

B. Find the fraction of the initial kinetic energy lost to friction. Relevance

A. Find the common speed.

Conservation of angular momentum L = Iω

for a uniform disc, moment of inertia is

I = ½mr²

initial angular momentum

L = ½(0.450)(0.031²)180(2π/60) + ½(0.270)(0.020²)0.0 = 1.811 x 10^-5‬

final angular momentum

1.811 x 10^-5‬‬ = (½(0.450)(0.031²) + ½(0.270)(0.020²))ω(2π/60)

ω = 144 rpm

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

angular kinetic energy is KEr = ½Iω²

KEi = ½(½(0.450)(0.031²))(180(2π/60))² = 0.0384 J

KEf = ½(½(0.450)(0.031²) + ½(0.270)(0.020²))(144(2π/60))² = 0.0307 J

fraction of KE lost to friction

R = (KEi - KEf) / KEi

R = 0.2001...

or almost exactly 20%

I hope this helps.

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