# Moment of Inertia Tensor about non-principal axis

I'm part of the Western Martial Arts/Historical European Martial Arts community, and a debate that often comes up is parrying with the edge vs parrying with the flat of a blade. I want to do some calculations myself to really convince myself one way or another.

Specifically what I'm looking to do is to calculate the moment of inertia tensor of a highly idealised sword (basically just the blade, tang and pommel treated as two rectangular prisms and a sphere) about some pivot.

My intention is to calculate the moment of inertia of each body individually, and find a way to sum them together; does the parallel axis theorem apply to the tensor quantity, or only to the scalar quantity? It is likely that the pivot point will not be about the principal axes.

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en.wikipedia.org/wiki/… – Jaime Nov 28 '12 at 4:02
I must've skipped over that when I looked. Thank you! – Daniel Blay Nov 28 '12 at 5:11
Actually, I'm not sure if that covers one of the other issues I'm having; can I sum together the respective MoI tensors of each part of the 'sword'? – Daniel Blay Nov 28 '12 at 7:19
You'll have to write the MoI matrix for each body wrt its CoM, then transform them using the PArallel Axis Theorem so they are referred to the common CoM, then you can add them together. – Jaime Nov 28 '12 at 8:54
So it is that simple. Wonderful! Thanks again. – Daniel Blay Nov 28 '12 at 9:13