Merry go round angular acceleration?

This is a conservation of angular momentum problem, not a conservation of energy problem, so use the angular momentum equation (angular momentum = moment of inertia * omega), not the rotational kinetic energy equation. Otherwise, though, all your logic and computations look correct. BTW, alpha is usually used to denote angular acceleration while omega usually denotes angular velocity (you used the right numbers in the right places, you just used the wrong symbol when you wrote out the basic equation).