# Angular motion

1. Mar 18, 2014

### mcheung4

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

2. Mar 18, 2014

### TSny

Hello, mcheung4.
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When a piece of dust flies out and sticks to the outer ring, what type of collision is that?

Would you expect kinetic energy to be conserved in this type of collision?

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Think about how the angular velocity of the inner ring will change with time. It might help to consider a related situation. Suppose you're standing on a platform that is free to rotate. You are initially rotating at an angular speed Ω with your arms outstretched and a mass m held in each hand. You then release the masses in your hands (without "throwing" the masses). What happens to your angular speed?