, who in 1835 published the first comprehensive mathematical analysis of the game, including descriptions of ball trajectories that remain fundamental to modern understanding. Core Physical Principles
During a collision between the cue ball and an object ball, the total momentum before and after impact is conserved (assuming negligible energy loss to heat and sound). For a direct hit: [ m_1 v_1i = m_1 v_1f + m_2 v_2f ] where both balls have identical mass ( m ). In a perfectly elastic collision, the balls exchange momentum, leading to the classic “30° rule” for cut shots.
When a ball with sidespin strikes a cushion, the friction between ball and cloth/rubber alters the rebound angle: