Angular momentum with mass flow

[benf.stokes]

Homework Statement

A drum of mass $$M_a$$ and radius a rotates freely with initial angular velocity $$\omega_a(0)$$. A second drum with mass $$M_b$$ and radius b >a is mounted on the same axis and is at rest, although it is free to rotate.
A thin layer of sand with mass $$M_s$$ is distributed on the inner surface of the smaller drum. At t=0, small perforations in the inner drum are opened. The sand starts to fly out at a constante rate $$\lambda$$ and sticks to the outer drum. Find the subsequent angular velocities of the two drums $$\omega_a$$ and $$\omega_b$$. Ignore the transit time of the sand

The Attempt at a Solution

I first tried to use conservation of angular momentum for the whole system but that got me nowhere because I need a second equation to solve for the angular velocities. I'm not sure you can use conservation of energy in this case, so I'm stuck.

 

[jbsteele]

I have been trying to find a way to use the momentum of the sand but I'm not sure how to.Any help would be greatly appreciated.