A disk of radius R and mass M is spinning at an angular velocity omega_o rad/s.

Question

A disk of radius R and mass M is spinning at an angular velocity omega_o rad/s. A non-rotating concentric disk of mass m and radius r drops on it from a negligible height and the two rotate together Find a relationship ( equation) for the final angular velocity omega. Now let: Determine the final angular velocity omega. What is the initial KE and the final KE of the system? Was KE conserved? The upper disk., initially at rest, falls with negligible speed on the lower one which is spinning. Their centers coincide.

Explanation / Answer

angular momentum is conserved

=> Li = Lf

=> I1W1 = I2W2

=> 1/2*(MR^2/2)*W1 = 1/2*(MR^2/2 + mR^2/2)*W2

=> 1/2*((2*(0.5)^2)/2)*10 = 1/2*(((2*(0.5)^2)/2) + (0.5*(0.1)^2)/2)))*W2

=> W2 = 9.90 rad/s

KE intial = 1/2*((2*(0.5)^2)/2)*10^2 = 12.5 J

KE final =

1/2*(((2*(0.5)^2)/2) + (0.5*(0.1)^2)/2)))*9.90^2 = 12.37 J

=> energy is not conserved

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