Angular motion

1. The problem statement, all variables and given/known data

A ring of mass Mb, radius b, is mounted to a smaller ring of mass Ma, radius a and with the same centre, and they are free to rotate about an axis which points through this centre and is perpendicular to the rings. Dust of mass Ms is distributed uniformly on the inner surface of Ma. At t=0, Ma rotates clock-wise at angular speed Ω while Mb is stationary. At t=0, small perforations in the inner ring are opend, and the dust start to fly out at a constant rate λ and sticks to the outer ring. Find the subsequent angular velocities of the 2 rings ωa and ωb. Ignore the transit time of the dust.

2. Relevant equations

Conservation of angular momentum.
Conservation of kinetic energy.

3. The attempt at a solution

(Ma + Ms)a2Ω = (Ma+Ms-λt)a2ωa + (Mb+λt)b2ωb

(Ma + Ms)a2Ω2 = (Ma+Ms-λt)a2ωa2 + (Mb+λt)b2ωb2

I tried to solve the system and both velocities turned out to be zero. Am I doing anyhting wrong?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

http://ift.tt/1g53Ems

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