Question on moment of inertia of multiple bodies

Main Question or Discussion Point

My boss and i were considering he following problem (see attached image):

2 unequal masses rotate an equal distance, r, about an axis. We both agreed that regardless of their angular position from eachother (wether they were diametrically opposed or otherwise oriented, the 2 examples shown in the image) is not relevent to their moment of inertia. However, you should be able to calculate the MOI using their center of mass and its distance, x, from the rotation axis. There is obviously something wrong with this assumption, since r and x are not equal. Can someone shed some light on this? Also, I am ignoring their centroidal mass moments.

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the MOI is about an axis of rotation. Not about the CG. (Well, it can be if you take the distances about the CG).

They should be the same to me. What you have in your example is the polar MOI.

I would expect the case where the CG is furthers from the axis of rotation (O) to have the most rotational imbalance.

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However, you should be able to calculate the MOI using their center of mass and its distance, x, from the rotation axis.
The MOI of a composite body about some axis does not simply = (total mass)*(distance from axis to center of mass)^2. To use the center of mass, you have to first find the MOI of the composite body about its center of mass and then use the parallel axis theorem to get the MOI about the desired axis. Do it properly and you'll find that you get the same total MOI this way or by just adding the individual MOIs.

Thanks for the help. I got it