A round disk of mass M and radius R is rotating around an axis right through its

Question

A round disk of mass M and radius R is rotating around an axis right through its center with a constant angular velocity. Another round disk of the same mass M but a smaller radius R/2 is initially not rotating but then dropped on the first disk with their centers on top of each other. The second disk then becomes rotating together with the first disk with a constant angular velocity. We assume that there is no external torque on the system.

1. Is the angular momentum conservered? and is the total kinetic energy conserver?

2. The final angular velocity is given by what equation?

Explanation / Answer

1)angular momentum conserved but not kinetic energy

2) final velocity = I1w1/(I1+I2)

=> w =( MR^2/4)*w /(MR^2/4 + MR^2/14)

w is the initial angular velocity of the bigger disk

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