It is a known fact that every rigid body has a set of orthogonal axes called principle axes about which when rotated the angular momentum vector and the angular velocity vector point in the same direction. Inside the body we can take any point as the origin and find a combination such that the products of inertia vanish with respect to that point. So, in that sense this set of principle axes is not unique, isn’t it? Feynman in his lectures has stated that the principal axes always pass through the centre of mass. Is this a necessary condition satisfied by the principal axes?