A 107 kg 107 kg horizontal platform is a uniform disk of radius 1.77 m 1.77 m and can rotate about the vertical axis through its center. A 63.1 kg 63.1 kg person stands on the platform at a distance of 1.11 m 1.11 m from the center, and a 27.9 kg 27.9 kg dog sits on the platform near the person 1.31 m 1.31 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.