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------------------------------------------------ A 103 kg horizontal platform is a uniform disk with a radius of 1.71 m and can rotate about the vertical axis through its center. A 68.9 kg person stands on the platform at a distance of 1.09 m from the center, and a 27.7 kg dog sits on the platform near the person, 1.45 m from the center. Find the moment of inertia of this system, consisting of the platform and its occupants, with respect to the axis.

To find the moment of inertia of the system consisting of the platform and its population, we must consider the contributions from the platform, the person, and the dog.

The moment of inertia of a uniform disk can be found using the formula I = 0.5 * mass * radius^2. For the platform, this becomes I_platform = 0.5 * 103 kg * (1.71 m)^2 = 161.45 kg*m^2.

The moments of inertia for the person and the dog can be found using the same formula. For the person, I_person = 0.5 * 68.9 kg * (1.09 m)^2 = 40.34 kg*m^2. For the dog, I_dog = 0.5 * 27.7 kg * (1.45 m)^2 = 27.68 kg*m^2.

The total moment of inertia of the system is the sum of the individual moments of inertia: I_total = I_platform + I_person + I_dog = 161.45 kg*m^2 + 40.34 kg*m^2 + 27.68 kg*m^2 = 229.47 kg*m^2.