# Moment of inertia for a hollow cube. Rotating about diagonal opp corners

## Main Question or Discussion Point

Hi Folks,
I am designing a piece of kinetic scultpure that will involve cubes made from aluminium square tubing rotating around an axis that passes through two diagonal corners. I am trying to determine motor size to drive this thing, and to do that I need to know its moment of inertia.
Math is not a strong point for me AT ALL. I don't even know what the symbols in the calcualtions for determining moment of inertia simple shapes represent. So while I would like to understand the calculation I'd request that I am not bamboozled by the theory.

So lets begin. Lets say my material has a mass of Q per meter. The cube side has a length of L. Most confounding for me (as I have not found an example of this elsewhere) the axis of rotation passes through two diagonal corners.
So lets say a cube L of 1000mm and the tubing is 50mm x 50mm (not sure if this is important)

The axis of rotation is the thin light grey line in the next image..

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Any help is greatly appreciated.

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Let me start by asking what the moment of inertia for a rod is, and how the Parallel Axis Theorem might be utilized here. Consider that six of the rods are connected to the spin axis and six are not, but all have a relative angle of arcsin((1/3)^2) to the spin axis (check me on this).

I am sorry if these concepts may be foreign to you. Perhaps someone here would be more expert at relating the details than I.

Perhaps I should first ask whether your sculpture is meant to accelerate.

It will experience acceleration - depending on the motor drive I can fit to it. From stationary up to 360 RPM. The acceleration will be dependant on the power of the motors but does not have to be rapid.

For a cube (or similarly symmetrical structure), the moment of inertia is the same regardless of axis orientation, as long as the axis passes through the CofG.

I was just playing around in SolidWork and found this to be true (perhaps common knowledge here).

Should you still wish to calculate the mass moment of inertia it is much simpler than may have been expected.

360 RPM sounds kind of fast for a sculpture. Are you guarding it?

Certianly it'll be within a sealed enclosure.
Ok that makes sense that it is still through the cofg but ... its dimensions.. the space it revolves through are different than if the axis passed through the centre of two oppsed walls... so its moment of inertia is still the same or different?
Also given that the sides have large vancancies.. how do I do that?
Will solid works tell me the Moment of inertia? I've been considering trying the demo version.

Ok that makes sense that it is still through the cofg but ... its dimensions.. the space it revolves through are different than if the axis passed through the centre of two oppsed walls... so its moment of inertia is still the same or different?
Also given that the sides have large vancancies.. how do I do that?
Will solid works tell me the Moment of inertia? I've been considering trying the demo version.
The model I created showed that the mass moment of inertia for a cube or cubic structure is independent of the orientataion of the rotational axis. Wouldn't hurt for you to check with another source; I will likely do the same.
Yes, SW will calculate the mass moment of inertia of a model, though in this case, it can be calculated quite simply.