Ten girls, of mass m=35kg each, initially stand at different…

Ten girls, of mass m=35kg each, initially stand at different points on the rim of a merry-go-round (essentially a disk that spins).  The merry-go-round has a moment of inertia of 800 kgm^2 and a radius of 4.0m.  The merry-go-round has an initial angular velocity of 0.20 rad/s and rotates freely on frictionless bearings.  On a signal the girls all start to move toward the center of the merry-go-round until they reach a distance of 1.5m from the center, where they stand again.  Find the new angular velocity of the system (in rad/sec).