Surprising Behavior of Spinning Tops and Eggs on an Inclined Plane

Abstract

A spinning top or a spinning hard-boiled egg is fascinating to observe since both objects can remain upright for a relatively long time without falling over. If spun at sufficient speed on a horizontal surface, the spin axis rises to a vertical position and the bottom end tends to remain fixed in position on the surface. If the initial spin is insufficient, then the spin axis will not rise all the way to the vertical, in which case a spinning top or a spinning egg will precess slowly around a vertical axis. If the bottom end is rounded, as it is with an egg or with a top having a round rather than a pointed peg, then the vertical precession axis does not necessarily pass through the center of mass. Instead, the precession axis may be located several centimeters away from the center of mass, depending on the radius of the bottom end. As a result, the whole egg or the whole top then rolls along the surface in an approximately circular path, several centimeters in diameter. The essential physics is described in Ref. 1 and the references therein, and in the many more books and papers since the early 1900s quoted in each of the references therein.