Packet 8: Bonus 19
Continuous symmetries correspond to conservation laws according to a groundbreaking theorem devised by Emmy Noether (“NUR-thurr”). For 10 points each:
[10h] If this quantity does not depend on a coordinate, Noether’s theorem implies that the coordinate’s corresponding generalized momentum is conserved. An ODE partly named for Euler relates the derivative of this quantity with respect to a coordinate q to its derivative with respect to q dot.
ANSWER: Lagrangian
[10m] Noether’s theorem implies that systems conserve energy if and only if the Lagrangian is not dependent on this quantity. Impulse equals force integrated over this quantity.
ANSWER: time
[10e] Noether’s theorem also implies that this quantity’s conservation results from systems where the Lagrangian is position-invariant. This quantity is conserved in both inelastic and elastic collisions.
ANSWER: linear momentum [reject “angular momentum”]
<Science - Physics, Jonathan Ouyang> | VAULT II Packet 08
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 20 | 21.00 | 80% | 95% | 35% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Washington | Kentucky | 0 | 10 | 0 | 10 | M |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| VAULT II at Georgia Tech | 2026-01-24 | ✓ | 4 | 22.50 | 100% | 100% | 25% |
| Triangle Cup | 2026-03-13 | ✓ | 1 | 10.00 | 0% | 100% | 0% |
| VAULT II at Eden Prairie HS | 2026-03-13 | ✓ | 2 | 10.00 | 50% | 50% | 0% |
| VAULT II at UCSB | 2026-03-13 | ✓ | 3 | 26.67 | 100% | 100% | 67% |
| VAULT II at Harvard | 2026-04-30 | ✓ | 1 | 20.00 | 100% | 100% | 0% |
| VAULT II at MINT | 2026-06-19 | ✓ | 1 | 10.00 | 0% | 100% | 0% |
| VAULT II Stanford Online | 2026-07-17 | ✓ | 8 | 23.75 | 88% | 100% | 50% |