I need to Calculate the moment of inertia of the array of point objects shown in

Question

I need to Calculate the moment of inertia of the array of point objects shown in the figure below. Assuming the m masses are spheres of diameter 0.132m and masses of 1.8 kgs, while the M masses are discs of radius 0.672m that lie in the plane of the figure and have masses of 3.1 kgs. Treat all wires as rods of mass 0.0379kg and a negligible diameter. a) How do I find the moment of inertia on the vertical axis? b) How can I find the moment of inertia on the horizontal axis? c) And is the harder axis to acelerate the one with the highest moment of inertia?

Explanation / Answer

For any single (point) mass m the moment of inertia = m *r^2 About the vertical axis I = m * [(.5 m)^2 + (1.0 m)^2] + M *[(.5 m)^2 + (1.0m)^2] = (m + M) * [(.5 m)^2 + (1.0m)^2] = 4.9 kg * 1.25m^2 = 6.125 kg m^2 About the horizontal axis I = 2 * M * (.25 m)^2 + 2 * m * (.25m)^2 = 2 * (M + m) * (.25 m)^2 I = 2.45 kg m^2

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