A 137 kg horizontal platform is a uniform disk of radius 1.53 m and can rotate about the vertical axis through its center. A 68.7 kg person stands on the platform at a distance of 1.19 m from the center, and a 25.9 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 population, with respect to the axis.

The moment of inertia is  

Explanation:

From the question we are told that

    The  mass of the platform is   m =  137 kg

     The radius is  r  =  1.53 m

    The mass of the person is  

    The distance of the person from the center is  

    The mass of the dog is  

     The distance of the dog from the person

Generally the moment of inertia of the system is mathematically represented as

Where is the moment of inertia of the platform which mathematically represented as

substituting values

Also    is the moment of inertia of the person about the axis which is mathematically represented as

substituting values

Also    is the moment of inertia of the dog about the axis which is mathematically represented as

substituting values

Thus  

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explanation: