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Answer :
Final answer:
The moment of inertia of the system consisting of the platform and its population is 229.47 kg*m^2.
Explanation:
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.
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