On this problem I keep getting 250.26Kgm^2 but my homework is saying \"Incorrect

Question

On this problem I keep getting 250.26Kgm^2 but my homework is saying "Incorrect. You seem to have mistakenly introduced the factor 1/2 in the moments of inertia of the person and the dog."

A 137-kg horizontal platform is a uniform disk of radius 1.67 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 25.1-kg dog sits on the platform near the person, 1.37 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.

Explanation / Answer

Let

M = 137 kg, R = 1.67 m

m1 = 62.3 kg, r1 = 1.07 m

m2 = 25.1 kg, r2 = 1.37 m

Total moment of Inertia, I = I_disk + I_person + I_dog

= 0.5*M*r^2 + m1*r1^2 + m2*r2^2

= 0.5*137*1.67^2 + 62.3*1.07^2 + 25.1*1.37^2

= 309.5 kg.m^2

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