Equations · equation
Ninety-Degree Rule
Billiards · 1835
- Equation
- v_OB = v cos θ (along the line of centres); v_CB = v sin θ (along the tangent line)
- Field
- Billiards
- Year
- 1835
Symbols
v cue-ball speed at contact · θ the cut angle, between the cue ball's path and the line joining the two centres at contact · v_OB object-ball speed · v_CB cue-ball speed after impact, with no spin acting yet
Significance
Two equal balls, one at rest, no spin: after the hit they separate at a right angle. The object ball leaves along the line of centres — always, whatever else you do — and the cue ball keeps whatever was perpendicular to that. It is momentum and energy conservation with equal masses, and it is a projection: cos θ of the speed goes one way, sin θ the other, cos²θ of the energy to the object ball. A half-ball hit (θ = 30°) sends 75 % of the energy on. Coriolis set it down in 1835. Real balls bend it a degree or two (restitution, throw), and spin bends the cue ball's path afterwards — but the tangent line is where every cue-ball plan starts.
Referenced by
equation
skill
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