four children stand at edge of a circular horizontal platform that is free to rotate about a vertical axis. each child has a mass of 35 kg and are at positions that are a quarter circle from each other. the platform has a moment of inertia equal to 500 kg*m2 and a radius of 2.0 m. the system is initially rotating at 6.0 rev/min. the children walk toward the center of the platform until they are 0.50 m from the center. (a) what is the rotational speed of the platform when the children are at the 0.50 m positions? (b) what is the change in rotational kinetic energy of the system? {-116 j}