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physicsdude101
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Homework Statement
Three equal point masses, mass M, are located at (a,0,0), (0, a, 2a) and (0, 2a, a). Find the centre of mass for this system. Use symmetry to determine the principle axes of the system and hence find the inertia tensor through the centre of mass. (based on Hand and Finch, Chapter 8 Problem 9).
Homework Equations
$$I_{xx}=\sum_{i} m_i(y_i^2+z_i^2)$$ ,$$I_{xy}=-\sum_{i} m_i x_i y_i$$ and $$\mathbf{R_{CM}}=\frac{\sum_{i} m_i\mathbf{r_i}}{\sum_{i} m_i}$$
The Attempt at a Solution
I got that the centre of mass was (a/3,a,a) but I'm not sure how to find the principle axes using symmetry as I can't really visualise the 3D setup that well.