Tennis racket theorem: Difference between revisions

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The theorem describes the following effect: rotation of an object around its first and third [[Moment of inertia#Principal axes|principal axes]] is stable, whereas rotation around its second principal axis (or intermediate axis) is not.
 
This can be demonstrated by the following experiment: hold a tennis racket at its handle, with its face being horizontal, and throw it in the air such that it performs a full rotation around its horizontal axis perpendicular to the handle (ê<sub>2</sub> in the diagram), and then catch the handle. In almost all cases, during that rotation the face will also have completed a half rotation, so that the other face is now up. By contrast, it is easy to throw the racket so that it will rotate around the handle axis (ê<sub>1</sub>) without accompanying half-rotation around another axis; it is also possible to make it rotate around the vertical axis perpendicular to the handle (ê<sub>3</sub>) without any accompanying half-rotation.
 
The experiment can be performed with any object that has three different moments of inertia, for instance with a book, remote control, or smartphone. The effect occurs whenever the [[axis of rotation]] differs only slightly from the object's second principal axis; air resistance or gravity are not necessary.<ref>{{Cite book |url={{google books|plainurl=yes|id=uVSYswEACAAJ|page=151}} |title=Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction |last=Levi |first=Mark |publisher=American Mathematical Society |year=2014 |isbn=9781470414443 |pages=151–152}}</ref>