Some quantities are conserved — they don't change in an isolated system.
Collision lab — watch momentum survive the crash
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.