- #1

mcheung4

- 22

- 0

## Homework Statement

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.

## Homework Equations

Conservation of angular momentum.

Conservation of kinetic energy.

## 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?