I spoke yesterday in class about rotating solid bodies, in particular when the object is spinning around an axis not aligned with one of the principal axes of the moment of inertia tensor. The challenging point is that if you fix the axis of rotation then you get bearing forces or torques, but if you spin torque-free then the axis of rotation necessarily precesses. Of course the details are pretty hard for a student seeing this material for the first time; many of my colleagues would drop this from an intro course. But I love mechanical engineering, and this particular process comes up just about everywhere in our every-day experience. I can't help but talk about it!
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