This is a structured report based on the known concepts from The Physics of Pocket Billiards (commonly associated with the work of Dr. Robert G. "Bob" Jewett, Dr. Dave Alciatore, and others, often referenced in the billiards community). Since I cannot directly access or reproduce a specific PDF file, this report synthesizes the standard physics principles that such a document would cover.
When you first strike the cue ball, it slides without rolling (sliding friction). Over a short distance, table friction converts sliding into true rolling. The transition distance depends on initial velocity and µ (coefficient of sliding friction, ≈0.2–0.3 for pool cloth). A quality PDF would include the formula for rolling resistance and the time constant for spin decay.
Key Equation (Sliding to Rolling): t = (2v₀)/(7µg)
Where v₀ is initial velocity, µ is friction coefficient, and g is gravity. This explains why draw shots are easier on shorter distances. the physics of pocket billiards pdf
The first chapter of any physics-based billiards PDF defines the conservation of linear momentum. In an ideal world, pool balls are considered near-perfect elastic spheres.
The Formula: ( m_1v_1 = m_1v_1' + m_2v_2' )
Because all balls have identical mass (( m )), the equation simplifies to a vector relationship. The critical takeaway for the player (which the PDF explains with geometric proof) is the 90-degree rule: On a perfectly cut shot with no spin, the cue ball and object ball will scatter at exactly 90 degrees relative to each other. This is a structured report based on the
When the cue ball is rolling naturally (with follow) and strikes the object ball with a half-ball hit (where the edge of the cue ball aligns with the center of the object ball):
For a cutting shot, the cue ball’s path after impact is perpendicular to the object ball’s path (90° rule). This applies only when the cue ball is sliding (not rolling) at impact.
The core of billiards physics is the conservation of linear momentum. When the cue ball strikes a stationary object ball, the total momentum before and after the collision remains constant (assuming no external forces like spin or table friction during the microsecond of impact). When you first strike the cue ball, it
Equation: m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f
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 rails (cushions) act as compliant springs. The angle of incidence is approximately equal to the angle of reflection, assuming a rolling ball.
However, physics dictates modifications: