The sum in the last of these equations must have balancing positive and negativecontributions, expressing the intuitive idea that the mass is distributed symmetricallyabout the principal axes. In particular, any axis of rotational symmetry of a massdistribution is a principal axis. The first three equations show that the principalmoments are all positive, unless the mass is all concentrated on a mathematicalstraight line, which is impossible for a real physical body. It can also be seen fromthese equations that the principal moments of inertia satisfy the triangle inequalities
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