1. There is no torque so the angular momentum should be conserved: you can calculated the angular velocity (or tangential component of velocity) for the whole system when the sleeve just at the instant it get free. (You need to find the rotational inertia for the whole system first)

2. You can find the velocity in the radial direction from conservation of energy (No external force,too!).

3. You can calculate the total velocity with those two components calculated from the above steps.