Billiard Physics: Motion of a Cue Ball after Hit by a Cue Stick Horizontally

Abstract

Billiards and pool games provide an excellent medium to discuss several physics principles including Newton’s laws of motion, friction, impulse-momentum theorem, work-energy theorem, kinematics and dynamics of rotational motion, and rolling motion. This paper provides a complete analysis of the motion of a cue ball that is given a sharp impulse, which is parallel to the horizontal surface. The horizontal impulse, in this work, is restricted to be in the plane passing through the ball’s center of mass and the contact point such that it sets the ball in horizontal motion with no sidespin. The motion of the cue ball until it eventually starts to roll without slipping is analyzed for all different impulse points on the surface of the ball. These analyses provide physics instructors a set of exciting examples on the rolling motion.