A solid disk of radius R and mass 2.57 kg is spinning at angular velocity 66.6 r

Question

A solid disk of radius R and mass 2.57 kg is spinning at angular velocity 66.6 rpm about a vertical axis. A solid disk of radius 2R drops concentrically on the first (sort of like dropping an old-fashioned 33 rpm record on a 45 rpm one), so that eventually the two cease to slip relative to each other and end up spinning at 19.9 rpm. What is the mass of the second disk?

Explanation / Answer

from angular momentum conservation; initial angular momentum = final angular momentum => (m*R^2/2)*w = [(m*R^2)/2 + M*(2R)^2/2]*w' => (2.57*R^2/2)*66.6 = [(2.57*R^2/2) + (4*M*R^2/2)]*w' => 85.581 = (1.285 + 2*M)*19.9 => M = 1.508 kg

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