A 123kg horizontal platform is a uniform disk of radius 159

A 123-kg horizontal platform is a uniform disk of radius 1.59 m and can rotate about the vertical axis through its center. A 62.3-kg person stands on the platform at a distance of 1.07 m from the center and a 27.3-kg dog sits on the platform near the person, 1.35 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.

Solution

For the disk:
I = (1/2)MR^2 = (1/2)123*1.59^2 = 155.478 kg m2
For the person:
I=MR^2 = 62.3*1.07^2 = 71.327 kg m2
For the dog:
I=MR^2 = 27.3*1.35^2 = 49.754 kg m2

total moment of inertia = 276.559 kg m2