# Inertia matrix and centre of gravity of a set of rods

1. Mar 1, 2008

### Bucky

1. The problem statement, all variables and given/known data
Three uniform rods OA, OB, and OC, each of mass 3m and length a, lie along the x, y and z axes, respectivley. Show that the inertia matrix relative to Oxyz is

$Io = 2ma^2 \left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right)$
Determine the inertia matrix with respect to a parallel frame through the centre of mass G.

2. Relevant equations

3. The attempt at a solution

The proof was straightforward enough, but finding Ig has proven difficult. The book lists it as

$Ig = 1/4ma^2 \left(\begin{array}{ccc}6&-1&-1\\-1&6&-1\\-1&-1&6\end{array}\right)$

Our current problem is finding the centre of mass of the system. I thought it would be G(a/2, a/2, a/2), as each rod is of length a, but the answer lists this as G(a/6, a/6, a/6). Can anyone point out where I've gone wrong? Thanks.