2D Elastic Collision Simulator
A pool-table-like arena where discs of varying mass and radius collide with full elastic (or inelastic) physics. Click and drag to launch discs and watch momentum and kinetic energy conservation in action.
m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′
The Physics of Elastic Collisions
Conservation Laws
In an elastic collision, both momentum and kinetic energy are conserved. Momentum
conservation (p = mv) is always true for isolated systems, while kinetic
energy conservation (KE = ½mv²) distinguishes elastic from
inelastic collisions. In this simulator, the coefficient of restitution (e) controls
how much kinetic energy is preserved: e = 1 is perfectly elastic, while e < 1
loses energy to deformation, sound, or heat.
2D Collision Resolution
When two discs collide in 2D, we decompose their velocities along the collision normal (the line connecting their centers) and the tangential direction. Only the normal components change during the collision; tangential components remain the same, since we assume frictionless surfaces. The normal impulse is calculated from the relative velocity, the masses, and the coefficient of restitution.
Mass and Momentum Transfer
A light disc hitting a heavy one bounces back, transferring little momentum. A heavy disc hitting a light one barely slows down while the light one shoots away. Equal masses exchange velocities perfectly — the classic Newton's cradle effect. Try different mass ratios and watch the momentum vectors to see these principles in action.
Why This Matters
Elastic collision physics underpins particle physics (scattering experiments at CERN), astrophysics (gravitational slingshots), materials science (atomic-scale interactions), and everyday engineering (crash safety, billiards). The conservation laws demonstrated here are among the most fundamental principles in all of physics, arising from deep symmetries of space and time described by Noether's theorem.