Momentum must be conserved in this problem. We find the initial momentum in (1) and then an expression for the final momentum (3).
The velocities of the rims of all three must be equal since they are touching. This will give us three linear independent equations and three unknowns (6) and (7). We plug the equations for 
and 
into (7) and get (8), then solve for (11) and plug in the numbers. Once we have one of the angular speeds, we can plug that number in (6) and get the other two angular speeds.
