The initiation of motion begins with the cue tip striking the cue ball. The outcome depends on the impulse delivered and the height of the contact point relative to the ball's center of mass.
Since all billiard balls have nearly identical mass (approx. 170g for a standard 2.25-inch ball), the equation simplifies dramatically. For a straight-on (central) collision, the cue ball stops dead, and the object ball moves forward with the cue ball’s original velocity. For non-central collisions, the balls separate at a right angle—a fact derived from Newtonian mechanics and elastic collision theory. the physics of pocket billiards pdf
: When a cue ball hits an object ball, the collision is nearly elastic, meaning kinetic energy is mostly conserved. Conservation of Momentum The initiation of motion begins with the cue
From sliding to rolling: [ t_\textslide = \fracv_0\mu_k g ] [ x_\textslide = \fracv_0^22\mu_k g ] where ( \mu_k ) ≈ 0.04–0.06 for pool cloth. 170g for a standard 2
As a ball travels, the friction between the ball and the cloth creates rotational motion . A sliding ball eventually transitions into a "natural roll" due to this friction [16]. 📐 The Geometry of the Shot