A 42 kg dog is at the center of a large disk of radius 6.0 m. Initially, the disk rotates horizontally with an angular velocity of 0.82 rad/s about a vertical axis through its center. Afterward, the dog walks directly to the edge of the disk. Given that the moment of inertia of the disk is 870 kg·m², determine the total rotational kinetic energy of the system with the dog initially on the disk at the center first and then do the same for when the dog walks to the edge of the disk. Assume that the disk rotates without any friction.