Spherical Tippe Tops

Abstract

A tippe top (see Fig. 1) is usually constructed as a truncated sphere with a cylindrical peg on top, as indicated in Fig. 2(a). When spun rapidly on a horizontal surface, a tippe top spins about a vertical axis while rotating slowly about a horizontal axis until the peg touches the surface. At that point, weight is transferred to the peg, the truncated sphere rises off the surface, and the top spins on the peg until it is upright. A feature of a tippe top is that its center of mass, labeled G in Fig. 2, is below the geometric center of the sphere, C, when the top is at rest. That is where it will return if the top is tilted sideways and released since that is the stable equilibrium position. The fact that a tippe top turns upside down when it spins is therefore astonishing. The behavior of a tippe top is quite unlike that of a regular top since the spin axis remains closely vertical the whole time. The center of mass of a regular top can also rise, but the spin axis tilts upward as the top rises and enters a “sleeping” position.