The Proof Is in the Putting
The Physics Teacher
A s the saying goes, "You drive for show and putt for dough." You would think that physicists, with their superior knowledge of vectors, would make excellent putters. However, this often proves not to be the case. In an attempt to better understand how to "read the break" on a putt, my students and I conducted a series of experiments with a springloaded putting machine that applies an impulse to the equator of a golf ball in roughly the same manner as a conventional putter. In this note,
... ental data are compared with a simple theory of putting that excludes such things as: irregularities in the putting surface (e.g., spike marks), complex contours, dew on the grass, wind resistance, and possible ball hopping (i.e., momentarily losing contact with the green). In addition to these factors, this analysis ignores what golfers call the "grain" of the grass, or what we, in the plain language of physics, might call "textural anisotropy." In other words, this is a putting green that exists only in the mind of a physicist. To understand how the ball will roll over the green, once struck, it is necessary to know both the slope and the frictional characteristics of the green. In order to learn how to properly model the frictional force between the ball and the putting green, we took measurements on flat and level surfaces for both a putting green and a livingroom carpet. A battery-powered photogate was positioned along the track of the ball at various distances. It was then possible to compute the velocity of the ball at various positions along its path. The results of these measurements are shown in Figs. 1 and 2 . If a golf ball is struck by a putter so as to produce no initial spin, 1 then it will skid for a dis-tance x t until the frictional torque increases its angular velocity and it finally achieves the pure rolling-without-skidding condition: 2 This transition from skidding to rolling is more easily observed at a bowling alley. Sometimes a bowling ball is released with no initial spin and sometimes it's even released with backspin. To determine x t , the distance over which the ball skids before making the transition to pure rolling, some assumptions must be made. We start by assuming that the golf ball of mass m and radius R can be treated as a uniform solid sphere. 3 For simplicity, we further assume that the coefficient of rolling friction r is much smaller than the coefficient of kinetic friction k and that the ball is launched with no initial angular velocity. V o is the initial velocity, and V f is the velocity of the ball when it has first stopped skidding and is just beginning to undergo pure rolling. Then, applying the impulse equations for both linear and Fig. 1. Velocity data for a putted ball on a closely cropped carpet.