- #1

peripatein

- 880

- 0

## Homework Statement

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.

## Homework Equations

## The Attempt at a Solution

I realize 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?