Striking the bottom of the ball forces it to rotate backward while sliding forward. Upon collision, the forward momentum stops, and the backward rotation engages with the cloth, pulling the cue ball backward. 3. Lateral Spin: The Physics of "English"
Applying sidespin (English) introduces complex aerodynamic and frictional forces:
Striking the top of the ball forces it to rotate faster than its forward speed. After hitting the object ball, this forward rotation grabs the cloth, pulling the cue ball forward past the tangent line.
: A historical text-book that frames the game as a "scientific amusement" requiring mental discipline and analysis.
When the cue ball strikes an object ball at an angle, they separate at (for a perfectly elastic, frictionless collision). In reality, due to friction during contact, the angle is slightly less than 90° (typically 85–88°). the physics of pocket billiards pdf
: Spin (English) affects the ball's trajectory via "squirt" (deflection) and "swerve" (curve), while follow and draw create parabolic paths after impact. Cushion Interaction
Because the balls are of equal mass and possess a high coefficient of restitution (elasticity), they behave nearly ideally as perfectly elastic bodies in collision scenarios. The felt cloth provides a friction coefficient ($\mu$) that is low enough to allow sustained travel but high enough to generate the specific rotational behaviors (spin) that define the game.
In reality, collisions are not perfectly elastic. The coefficient of restitution ($e$) measures the "bounciness" of the collision. For high-quality phenolic resin billiard balls, $e \approx 0.95$ to $0.98$. This slight loss of energy results in the angle between the two balls being slightly less than 90 degrees, a phenomenon known as the "inelastic correction."
Banks and kicks are governed by the law of reflection: angle of incidence equals angle of reflection. However, real tables complicate this: Striking the bottom of the ball forces it
If you have searched for the phrase "the physics of pocket billiards pdf," you are likely looking for one of two things: the seminal work by Dr. Marlow (often considered the "Bible" of pool physics) or a general technical resource to download for offline study. This article serves as a guide to what that PDF contains, the key principles you will learn, and how to apply high-level physics to your game.
While idealized physics assumes perfect sliding, a real pool table introduces friction. Friction exists between the ball and the cue tip, the ball and the cloth, and between the balls themselves. Sliding vs. Rolling
If a cue ball is still sliding when it hits the object ball, it will follow the 90-degree tangent line perfectly. If it has transitioned into a natural roll, friction will cause the cue ball to curve forward, narrowing the angle to roughly 30 degrees (governed by ). The Effects of Vertical Spin
The Physics of Pocket Billiards: Unlocking the Science Behind the Table Lateral Spin: The Physics of "English" Applying sidespin
: The book is dense with equations and mathematical formulae . If you enjoy digging into calculus and physics to understand ball dynamics, it’s a goldmine.
The ideal would end with a "cheat sheet" of usable formulas:
Where ω is the spin rate and k is a cloth/rail constant. This is why professionals use running English (spin in the direction of travel) to shorten a bank and reverse English to lengthen it.