# Tensor of inertia – hollow cube.

Hi,

I have found the tensor of inertia of a rectangle of sides a and b and mass m, around its center, to be I

**1. The problem statement, all variables and given/known data**I have found the tensor of inertia of a rectangle of sides a and b and mass m, around its center, to be I

_{11}=ma^{2}/12, I_{22}=mb^{2}/12, I_{33}=(ma^{2}+ mb^{2})/12. All other elements of that tensor are equal to zero. I would now like to use this result to determine the tensor of inertia of a hollow cube of side a around its center of mass.
**2. Relevant equations**

**3. The attempt at a solution**

I realise I have to use the parallel axis theorem. I have hence tried the following:

I_{11}=ma^{2}/12 + m(a/2)^{2}, which yielded the wrong answer.

I know that the correct equation is I_{11}=I_{22}=I_{33}=ma^{2}/12+ma^{2}/12+ma^{2}/6+4(ma^{2}/12 + m(a/2)^{2})=5/3*ma^{2}

I simply do not understand why this is correct. Could anyone please explain why this is the correct way to calculate the desired tensor of inertia? Also, why would I be summing all the diagonal elements in my tensor for the rectangle?

http://ift.tt/1g1xFxG

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