Collision & Momentum Simulator
Smash discs together and discover the law that never breaks: total momentum is conserved in every collision, elastic or not.
This is real impulse-based 2D collision physics — no simplification. Pick a preset or drag on the table to launch a disc, then watch the system panel: total momentum stays constant through every disc-on-disc hit, while kinetic energy is only conserved when the collision is perfectly elastic (e = 1).
Presets
System
Selected disc
Tap a disc to read its mass, speed, momentum and kinetic energy, and adjust its mass.
Formulas & sources
p = Σ mᵢvᵢ (conserved)
j = −(1+e)·vᵣₑₗ,n / (1/m₁+1/m₂)
v₁′ = ((m₁−m₂)u)⁄(m₁+m₂) (1D, e=1)
v₂′ = (2m₁u)⁄(m₁+m₂) (1D, e=1)
The units behind this collision
A collision is bookkeeping in two currencies: momentum and energy. Neither has a unit of its own — both are built from kilograms, metres and seconds.
What you are changing
The same two currencies for everyday objects
| Object | Mass | Speed | Momentum p = mv | Energy E = ½mv² |
|---|---|---|---|---|
| Served tennis ball | 0.058 kg | 50 m/s | 2.9 kg·m/s | 73 J |
| Cyclist | 15 kg | 5 m/s | 75 kg·m/s | 188 J |
| City car | 1500 kg | 14 m/s | 21,000 kg·m/s | 147,000 J |
Calculated live from p = mv and E = ½mv². Notice the cyclist carries 26× the momentum of the tennis ball but only 2.6× the energy — momentum grows with v, energy with v².
Why both are conserved, but only one is always conserved
Momentum is conserved in every collision, elastic or not. Kinetic energy is conserved only when the collision is elastic — set restitution below 1 in the simulator and watch the energy readout drop while momentum stays put. The missing energy did not vanish; it became heat and sound, which the simulation does not draw.
How the SI units are defined →