Can someone help me solve this and show all of their work? thank you! Three smal

Question

Can someone help me solve this and show all of their work? thank you!

Three small spherical masses are located in a plane at the positions shown below. -1 -2 -4 -5-4- -2 -1 0 1 23 4 5 x (m) The masses are Q-0.500 kg, R-0.300 kg, and S-0.600 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through X-0 and y--1. [Since the masses are of small size, you can neglect the contribution due to moments of inertia about their centers of mass.]

Explanation / Answer

The moment of inertia of the entire system would be the sum of each individual moment of inertia.
I(Q)=m(r^2)
= m*(sqrt((y2-y1)^2 + (x2-x1)^2)^2
= 0.500kg * sqrt[(-1-2)^2 + (4^2)]
= 2.5

I(R) = 0.300*sqrt((-1-5)^2 + (0)^2)
= 1.8

I(S) = 0.6*sqrt[(-1-1)^2+(-3)^2)]
=2.1633

Inet = I(Q) + I(R) + I(S)
= 6.5 kg/m^2

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