Moment of inertia tensor

  • #1
281
0

Homework Statement


Compute the moment of inertia tensor I with respect to the origin for a cuboid of constant mass density whose edges (of lengths a, b, c) are along the x,y,z-axes, with one corner at the origin.

The Attempt at a Solution


I get

[tex]I = M \left(
\begin{array}{ccc}
\frac{1}{3} (b^2+c^2) & -\frac{ab}{4} & -\frac{ac}{4}\\
-\frac{ab}{4} & \frac{1}{3} (a^2 + c^2) & -\frac{bc}{4}\\
-\frac{ac}{4} & -\frac{bc}{4} & \frac{1}{3} (a^2 + b^2)
\end{array}
\right)[/tex]

Can this be right?
 

Answers and Replies

  • #2
radou
Homework Helper
3,115
6
I think it may be right, since the matrix is supposed to be symmetric.
 
  • #3
281
0
Yeah, but it can be symmetric in many ways. ;)

Can someone please explain the equality

[tex]\int_V \rho(\vec{r}) (r^2 \delta_{jk} - x_jx_k) dV = \int_V \rho(x,y,z)
\left(
\begin{array}{ccc}
y^2+z^2 & -xy & -xz\\
-xy & z^2+x^2 & -yz\\
-xz & -yz & x^2+y^2
\end{array}
\right)dxdydz[/tex]

for me? I think this is the most important step in my understanding for this problem.
 

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