Physics and billiards

Published : Jan 18, 2008 00:00 IST

CLASSICAL mechanics is the mathematical study of the motions of real or imagined objects, be they heavenly bodies, molecules of air, ships and waves on the sea, falling snowflakes, spaceships, cones rolling on one another, or so on. Understanding classical mechanics is an absolute prerequisite for the mastery of physics, geology, astronomy or engineering. There can be no more pleasurable introduction to its principles than the games of pool and billiards, which require sharp eye and steady hand, but also profound physical intuition. This monograph inspired by many youthful hours spent in Cornell Universitys game room introduces a variety of mathematical methods and applies them to the motions and impacts of hypothetical spherical bodies, and in some cases, to the very real play of balls upon a billiard table and their interactions with cues, cushions and one another.

With two big differences, the game of billiards is akin to elementary particle physics as played at giant accelerators, where subatomic particles are made to collide with one another. Because billiard balls are much bigger than atoms, quantum mechanical uncertainty is irrelevant to their motion we may imagine shots set up with arbitrary precision. Because billiard balls travel much less swiftly than light, relativistic effects (and Einsteins famous formula E = Mc{+2}) are irrelevant as well we need never fear a collision of two billiard balls to produce a third. The game of billiards illustrates Newtons laws in action and serves as an introduction to many of the simple yet powerful tools of mathematical physics. The renowned physicist and popular author Freeman Dyson offered an unintended tribute to the subject matter of this book: Natural philosophy, as I learned it, consisted of solving problems about rough spheres rolling and spinning without sliding on rotating turntables.

Physics and the Game of Billiards may enrich the game for pool sharks and billiards aficionados. It may amuse and educate fanciers of the liberal arts who dabble in things scientific. However, our monograph is intended primarily as an adjunct to an introductory physics course directed toward students with a possible interest in physics or engineering as a career. Calculus is used sparingly and only when necessary, but mathematical techniques are developed that have wideranging application: not only in physics but in related disciplines such as space science, sports science and ballistics. Many illustrative exercises are provided, some very simple, some quite subtle.

Sheldon Glashow
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