The Revolving Jigsaw Piece
This is a regular jigsaw puzzle piece. It is based on a square, and has two "in" and two "out" connectors.
If you toss this puzzle piece in the air with some spin, around which axis can it rotate in a (reasonably) stable manner?
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1 solution
It is a well-known fact in rotational mechanics that a body can rotate stably about two of its three principal axes. If the moments of inertia relative to the three axes are I 1 < I 2 < I 3 , then the stable axes of rotation are axes 1 and 3.
The puzzle piece has its largest moment of inertia around the z -axis, perpendicular to the surface. Around this axis stable rotation is possible.
The puzzle piece has its smallest moment of inertia around the y -axis: the two "in" connectors bring the mass closer to the axis than for a square without holes. Likewise, the medium moment of inertia is around the x -axis.
Thus we can expect (somewhat) stable rotation around the y -axis .