Motions of a billiard ball after a cue stroke

TL;DR

This paper analyzes the physics of billiard ball collisions, deriving velocities and the squirt angle to understand how the ball deviates after impact, providing insights into cue-ball dynamics.

Contribution

It presents a detailed model of the collision process, including rotational velocities and squirt angle calculation, which is a novel analytical approach in billiard physics.

Findings

Derived formulas for post-collision velocities.

Calculated the squirt angle for oblique impacts.

Enhanced understanding of cue ball deviation.

Abstract

We study the collision between the cue and the ball in the game of billiards. After studying the collision process in detail, we write the (rotational) velocities of the ball and the cue after the collision. We also find the squirt angle of the ball for an oblique collision which represents the deviation of the ball from the intended direction.