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Homework Help: Moment of inertia tensor

  1. Nov 30, 2006 #1
    1. The problem statement, all variables and given/known data
    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.

    3. 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?
     
  2. jcsd
  3. Nov 30, 2006 #2

    radou

    User Avatar
    Homework Helper

    I think it may be right, since the matrix is supposed to be symmetric.
     
  4. Nov 30, 2006 #3
    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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