Review DOI: 10.1002/jst.88 Performance versus moment of inertia of sporting implements Rod Cross 1 and Alan M. Nathan 2,Ã 1 Physics Department, University of Sydney, Australia 2 Department of Physics, University of Illinois, USA A review is presented of the importance of the moment of inertia (MOI) to the performance of a sporting instrument. It is shown that for a given coefficient of restitution (COR), both the intrinsic power and the swing speed of a tennis racquet or baseball bat correlate strongly with the MOI about an axis through the handle and only weakly with the mass. It is further shown that for non-wood baseball bats approved for use in college baseball in the USA, batted ball speed is a stronger function of COR than of MOI. When comparing two implements with the same MOI, the primary factor affecting performance is the COR, which can be enhanced by means of the trampoline effect. A new method of matching the MOI of a set of golf clubs is also described. r 2009 John Wiley and Sons Asia Pte Ltd 1. INTRODUCTION The physics of sporting implements has been considered in journal articles [1–4] and in several books on the subject [5–9]. There is one particular aspect that has not received as much attention as it deserves, despite the fact that it is foremost on the minds of many players. That is, how does the performance of a sporting implement depend on its physical properties? A common view is that heavy implements are more powerful than light instruments. Moreover, heavy instruments cannot be swung as fast as light instruments. Both statements are technically incorrect. Most implements used in any particular sport tend to be similar in weight, in which case the common view can be both misleading and of no help when comparing implements of the same weight. The primary factor determin- ing both power and swing speed, regardless of the mass of the implement, is its moment of inertia (MOI). In this review, it is shown why this is the case, giving specific examples from baseball, tennis, and golf. The MOI of a sporting implement is not as well-defined as its mass or length since it depends on the arbitrary axis chosen to measure it. Moreover, the chosen axis is not necessarily the one chosen by a player to swing it. For practical convenience and consistency, the MOI of a baseball bat is conventionally measured by swinging the bat about an axis within the handle located 15 cm (6 inches) from the knob end. Similarly, the MOI of a tennis racquet is conventionally measured by swinging the racquet about an axis in the handle located 10 cm (4 inches) from the end of the handle. In this paper, we will denote the conventional MOI of a bat or racquet as I 15 or I 10 , respec- tively, and following colloquial usage, will refer to it as the ‘swing weight’. It can be measured by swinging the implement in a vertical plane as a physical pendulum and measuring its period of oscillation. Together with the mass and center of mass location, the period determines the MOI about the pendulum axis. Alternatively, the implement can be swung in a horizontal plane using a calibrated spring to provide a re- storing force, in which case there is no need for any additional measurements of the mass and center of mass location to de- termine the swing weight. There is an established tradition in golf that the numbered irons in a set of clubs differ in length by increments of 1.3 cm (0.5 inches) and that each club is matched by having the same first moment of the mass distribution, denoted herein by S 1 , relative to an axis in the handle located 35.5 cm (14 inches) from the end of the handle [8]. The matching can be achieved by increasing the mass of the club head in increments of approximately 7 g (1/4 oz) to compensate for the decreasing length of each club. It was established in the 1930s that clubs matched in this manner feel much the same when they are *Department of Physics, University of Illinois, Urbana, IL 61801, USA. E-mail: a-nathan@illinois.edu Keywords: . tennis . baseball . golf . performance . moment of inertia Sports Technol. 2009, 2, No. 1–2, 7–15 & 2009 John Wiley and Sons Asia Pte Ltd 7 Performance versus moment of inertia