# Angular motion

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

A ring of mass M_{b}, radius b, is mounted to a smaller ring of mass M_{a}, 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 M_{s} is distributed uniformly on the inner surface of M_{a}. At t=0, M_{a} rotates clock-wise at angular speed Ω while M_{b} 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 ω_{a} and ω_{b}. Ignore the transit time of the dust.

**2. Relevant equations**

Conservation of angular momentum.

Conservation of kinetic energy.

**3. The attempt at a solution**

(M_{a} + M_{s})a^{2}Ω = (M_{a}+M_{s}-λt)a^{2}ω_{a} + (M_{b}+λt)b^{2}ω_{b}

(M_{a} + M_{s})a^{2}Ω^{2} = (M_{a}+M_{s}-λt)a^{2}ω_{a}^{2} + (M_{b}+λt)b^{2}ω_{b}^{2}

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**

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