Math Playground
Physics

Conservation laws

Energy, momentum, charge — quantities the universe insists on keeping.

Some quantities are conserved — they don't change in an isolated system.

Collision lab — watch momentum survive the crash
2kg1kg
Momentum before
115
Momentum now
115
Kinetic energy before
5213
Kinetic energy now
5213

Watch the bars. Momentum is conserved in every collision.

Quick check

A ball is dropped and bounces back to a lower height than it started. What happened to the 'missing' energy?

What's conserved (in an isolated system)

  • Energy — total stays constant; it only changes form.
  • Momentum — total p = Σm·v is unchanged with no external force.
  • Angular momentum — why a spinning skater speeds up when arms pull in.
  • Electric charge — never created or destroyed, only moved.

Each conservation law mirrors a symmetry of nature (Noether's theorem): energy ↔ time-invariance, momentum ↔ space-invariance, angular momentum ↔ rotation-invariance.

Recap
  • Conserved means 'the total doesn't change', not 'each part stays the same'.
  • Energy converts between kinetic, potential, thermal, etc.
  • These laws hold even when you can't track every detail.

Conserved quantities

  • Energy.
  • Momentum.
  • Angular momentum.
  • Electric charge.

Each conservation law connects to a symmetry, via Noether's theorem.