A 103 kg horizontal platform is a uniform disk of radius 1.73 m and can rotate about the vertical axis through its center. A 61.7 kg person stands on the platform at a distance of 1.01 m from the center, and a 25.3 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.

The moment of inertia of the platform can be calculated using the formula for a uniform disk, which is given by:
I_disk = (1/2) * m * r^2
where m is the mass of the platform and r is its radius. Plugging in the values given in the question, we have:
I_platform = (1/2) * 103 kg * (1.73 m)^2
Next, we need to calculate the moment of inertia of the person. The moment of inertia of a point mass is given by:
I_point mass = m * r^2
where m is the mass of the point mass and r is its distance from the axis of rotation. Plugging in the values given in the question, we have:
I_person = 61.7 kg * (1.01 m)^2
Finally, we need to calculate the moment of inertia of the dog. Using the same formula as above, we have:
I_dog = 25.3 kg * (1.45 m)^2
Now, we can add all the moments of inertia together to get the total moment of inertia of the system:
I_system = I_platform + I_person + I_dog
Substituting the values we calculated earlier, we get:
I_system = (1/2) * 103 kg * (1.73 m)^2 + 61.7 kg * (1.01 m)^2 + 25.3 kg * (1.45 m)^2
Calculating this expression will give us the moment of inertia of the system.

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