Momentum Billiards — The Physics Behind the Game
Billiards is one of the purest demonstrations of momentum conservation in everyday life — every shot, every collision, every ball that stops dead while another shoots forward is the direct, visible consequence of a single unbreakable law: total momentum before a collision always equals total momentum after. Momentum Billiards puts real 2D collision physics under your cue, letting you feel how mass, angle, and speed determine exactly where every ball ends up.
How to Play
- Drag from the cue (white) ball in the direction you want to shoot
- Release to strike — shot power depends on how far you drag
- Sink the required coloured ball(s) in a pocket without scratching (sinking the cue ball)
- Use as few shots as possible for a higher star rating
- Press R to reset the level at any time
The Physics Behind the Game
Every collision in this game obeys conservation of momentum: m₁v₁ + m₂v₂ (before) always equals m₁v₁′ + m₂v₂′ (after). In elastic collisions (the default mode), kinetic energy is also conserved, which produces the classic "stun shot" you'll see in Level 1 — when a moving ball strikes an identical stationary ball dead-on, the moving ball stops completely and the stationary ball takes on all of its velocity. This isn't a scripted animation; it's the exact mathematical solution to conservation of momentum and kinetic energy for two equal masses.
For off-centre "cut" shots, momentum splits along two directions: the target ball moves along the line connecting the two ball centres at the moment of impact, while the cue ball deflects to preserve the sideways component of momentum — for equal masses in an elastic collision, these two paths are always exactly perpendicular to each other, a genuinely useful rule real billiards players learn intuitively through practice.
Level 6 switches to inelastic mode, where colliding balls stick together and move as one afterward. Momentum is still conserved — v′ = (m₁v₁ + m₂v₂)/(m₁+m₂) — but kinetic energy is not; some is lost to deformation, heat, and sound at the moment of impact. Comparing the elastic and inelastic levels side by side is one of the clearest ways to build intuition for the difference between these two collision types.
What You'll Learn
By the end of the eight levels, you'll have direct, hands-on intuition for: how momentum transfers in head-on and off-centre collisions, why elastic and inelastic collisions behave so differently, how cushion (wall) bounces reflect exactly like light off a mirror, how momentum chains work when one ball strikes another which strikes another, and how rolling friction gradually removes kinetic energy from a moving ball — the same physics used throughout the site's Momentum and Impulse & Momentum calculators.
Level Guide
Levels 1-2 establish the basic stun shot and cut shot with a single target. Levels 3-4 introduce cushion bounces and momentum-chain combo shots. Level 5 requires planning across multiple shots to sink two balls. Level 6 switches to inelastic collisions with a "sticky" ball. Level 7 is a long-distance friction-judgment shot, and Level 8 combines everything — angled contact, a combo chain, and a strict shot limit — into one final challenge.
Real-World Connections
Momentum conservation in collisions isn't just a billiards curiosity — it's the exact physics engineers rely on to design vehicle crumple zones, analyse traffic collisions, and predict particle behaviour after a nuclear or subatomic collision. Newton's cradle, the classic desk toy, demonstrates the identical stun-shot physics you'll see in Level 1, just with hanging steel balls instead of billiard balls — pull back one ball, release it, and only the ball on the far end swings out, carrying away the exact momentum delivered by the first.
Professional billiards and pool players develop deep intuition for exactly this physics without ever writing down an equation — reading angles, judging power, and predicting cue-ball position after contact are all momentum-conservation problems solved through practised feel, which is precisely the intuition this game is designed to build.
Why Elastic Collisions Produce the Stun Shot
The stun shot you'll encounter in Level 1 looks almost like a magic trick the first time you see it — the cue ball strikes the target dead-on and simply stops, as if it hit an invisible wall, while the target ball shoots away carrying the cue ball's entire original speed. It isn't magic; it's the unique mathematical solution when two equal masses collide elastically head-on. Solving the two conservation equations (momentum and kinetic energy) simultaneously for equal masses always gives this exact result: the velocities completely swap. This is why the stun shot is such a reliable, repeatable technique for real pool and billiards players — it's not a matter of skill or luck, it's a direct consequence of the underlying physics working out to a single, unambiguous answer every time.
If the masses aren't equal, the outcome changes: a heavier cue ball striking a lighter target won't stop completely — it continues forward at reduced speed, while the lighter target shoots off faster than the cue ball's original speed. A lighter cue ball striking a heavier target can even bounce backward. All of these outcomes emerge from exactly the same two conservation equations, just with different mass ratios substituted in — which is precisely why the "blocker" ball in Level 3 (three times the mass of a normal ball) behaves so differently on contact than an equal-mass ball would.
Cushion Bounces and the Law of Reflection
When a ball strikes a cushion (the rail around the table edge), the component of its velocity perpendicular to the rail reverses, while the component parallel to the rail is unaffected — exactly the same reflection law that governs light bouncing off a mirror, angle of incidence equals angle of reflection. A small amount of energy is lost to the cushion's slight give on each bounce (captured in the game by a restitution coefficient just under 1), which is why balls gradually lose a little speed with each rail contact, just as real billiard cushions do.
Learning to predict cushion bounce angles is one of the most valuable spatial-reasoning skills the game builds — Level 3's bank shot specifically requires calculating where a ball must strike the rail so that its reflected path arrives precisely at the target, a calculation professional players make instinctively but which follows directly from this simple reflection rule.
Friction and the Delicate Touch
Every ball on the table loses speed continuously to rolling friction — a resistive force proportional to the ball's current speed that steadily removes kinetic energy the longer the ball keeps moving. This is why Level 7 rewards a soft, well-judged shot over a hard one: hit the cue ball too gently and it stops before reaching the target; hit it too hard and it overshoots or bounces off the far cushion with too much energy remaining to be predictable. Somewhere in between lies the precise power that lets friction bring the ball to rest exactly where you need it.
This friction model is deliberately simplified compared to the full physics of a rolling ball (real billiard balls also experience spin-dependent effects like draw and follow, where backspin or topspin changes how the ball behaves after contact), but the core lesson — that resistive forces steadily bleed energy from a moving object — is exactly the same principle covered in the site's Terminal Velocity calculator, just applied to rolling resistance instead of air drag.