Pool Break

The physics of pool: sliding, rolling and spin

A pool table looks like a game of angles, but much of the skill is about spin. Every ball on the cloth is either sliding, rolling or doing a bit of both, and that decides what happens when it meets another ball.

Sliding becomes rolling

Hit the cue ball dead in the centre and it leaves the tip with no spin. It skids across the cloth, and friction at the point of contact drags its bottom backwards. That friction slows the ball and, because it acts below the centre, sets it turning. Within a short distance the turning catches up with the motion and the ball rolls naturally, with no slip at all. For a solid ball this always happens at five sevenths of the starting speed. After that only a much smaller rolling resistance slows it down.

Stun, follow and draw

When two equal balls meet full on, the moving one hands over its forward speed and stops, just like the balls of a Newton’s cradle. A cue ball that is still sliding when it arrives therefore stops dead: the classic stun or stop shot. If it has already started rolling, its forward spin survives the collision, grips the cloth and drives it on after the object ball: a follow shot. Strike it low and the ball carries backspin. If some backspin is left at contact, it pulls the cue ball back towards you: a draw shot. Distance matters, because the cloth wears spin away, so a draw that works over a short distance can fade to nothing over a long one.

Angles and cushions

On a thinner hit the object ball always sets off along the line joining the two centres at the moment of contact, which is what the guide shows. A cue ball with no spin then leaves at close to right angles to it, while a rolling cue ball bends forward, ending up around 30 degrees from its original line for a wide range of cuts. Cushions give back most of a ball’s speed but not all, and friction at the rubber nose turns side spin into a change of rebound angle. That is how players steer the cue ball around the table.

The break

A good break sends the cue ball into the rack at several metres per second. The rack is tight, so the push passes through ball after ball in a tiny fraction of a second and spreads the pack across the table. A firm, square hit with little spin hands on the most energy.

For the curious

A ball of radius R slips at its contact point with velocity u = v + ω × r, where r points from the centre down to the cloth. Sliding friction μ_sg, with μ_s ≈ 0.2, acts against u. Because the moment of inertia is I = 2⁄5 mR², the slip shrinks at 7⁄2 μ_sg, so rolling begins after t = 2|u₀|/(7μ_sg). A cue hit with the tip a·R to the side and b·R above the centre gives speed V and spin ω = (5V/2R)(a ŷ + b ŷ × d̂), where d̂ is the aim; b = 2⁄5 is exactly natural roll. Here the balls collide with a restitution of 0.94 and the cushions with 0.78.