(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to calculate the kinetic energy of a rotating cube about one of its face diagonals, using the moment of inertia tensor for the cube rotating around one of its corners.

2. Relevant equations

T=[itex]\frac{1}{2}[/itex][itex]\omega[/itex][itex]\cdot[/itex]L

L=I[itex]\omega[/itex]

(I'm not sure how to signify vectors in this interface, but I realize I'm dealing with vectors...)

3. The attempt at a solution

What I'm confused about is getting the moment of inertia tensor to apply to rotating about the face diagonal. There is an example in the book where they are using the moment of inertia tensor about a corner to calculate angular momentum around the cube's main diagonal. The author introduces a unit vector, u, in direction of rotating which he defines as u=([itex]\frac{1}{\sqrt{3}}[/itex])(1, 1, 1). Then the problem follows naturally. I believe the problem I'm dealing with can be solved similarly, though I'm not understand exactly what this unit vector represents. Can anyone explain it to me?

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# Homework Help: Kinetic energy of a rotating cube

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