Equations · equation
Slide to Roll
Billiards · 1835
- Equation
- rolling when v = ω R; a stunned ball rolls after t = 2 v₀ / (7 μ_s g), at 5/7 of its speed
- Field
- Billiards
- Year
- 1835
Symbols
v linear speed · ω spin · R radius · v₀ speed at the start of the slide · μ_s sliding friction on cloth, about 0.2 · g gravitational acceleration
Significance
A ball struck at centre skids first — no spin, so the cloth drags its bottom and spins it up while slowing it down — until the surface speed matches the ball's speed and it rolls. It loses two-sevenths of its speed getting there, in a distance that scales with v₀². Topspin shortens the skid, backspin reverses it: a drawn cue ball skids backward-spinning, stops spinning, then rolls back the way it came. Every follow and draw shot is this transition happening after the collision instead of before it.
Referenced by
equation
skill
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.