The rise and fall of spinning tops

Abstract

The motion of four different spinning tops was filmed with a high-speed video camera. Unlike pointed tops, tops with a rounded peg precess initially about a vertical axis that lies well outside the top, and then spiral inward until the precession axis passes through a point close to the center-of-mass. The center-of-mass of a top with a rounded peg can rise as a result of rolling rather than sliding friction, contrary to the explanation normally given for the rise of spinning tops. A tippe top was also filmed and was observed to jump vertically off a horizontal surface several times while the center-of-mass was rising, contrary to the usual assumption that the normal reaction force on a tippe top remains approximately equal to its weight. It was found that the center-of-mass of a tippe top rises as a result of rolling friction at low spin frequencies and as a result of sliding friction at high spin frequencies. It was also found that, at low spin frequencies, a tippe top can precess at two different frequencies simultaneously.