Packet J: Bonus 16
In tensorial form, these equations can be written as “I omega-dot plus omega cross the quantity I times omega” equals tau. For 10 points each:
[10h] Name these equations that relate the three principal moments of inertia to components of the angular velocity, angular acceleration, and torque vectors.
ANSWER: Euler (“OY-ler”) equations [or Euler’s equations; reject “Euler-Lagrange equations”]
[10e] The Euler equations can be derived from the fact that torque equals the time derivative of this quantity. Physics teachers often tilt a spinning bicycle wheel to demonstrate the conservation of this quantity.
ANSWER: angular momentum [prompt on L; reject “momentum”]
[10m] The bicycle wheel in the demonstration acts like one of these devices that contain a rotor spinning in a constant direction. Gravity can exert an external torque on these devices, causing them to precess.
ANSWER: gyroscopes [accept gyroscopic precession; prompt on tops by asking, “what devices do they behave like?”]
<Editors, Physics> | Packet J
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 126 | 15.40 | 84% | 65% | 5% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Durham B | Edinburgh B | 0 | 10 | 10 | 20 | EM |
| Durham D | Edinburgh D | 0 | 0 | 10 | 10 | M |
| Edinburgh A | Sheffield A | 0 | 10 | 10 | 20 | EM |
| Edinburgh C | Durham A | 0 | 10 | 10 | 20 | EM |
| Sheffield B | Durham C | 0 | 10 | 10 | 20 | EM |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| Northern California | Main | ✓ | 4 | 20.00 | 100% | 100% | 0% |
| Southern California | Main | ✓ | 7 | 17.14 | 100% | 71% | 0% |
| Eastern Canada (1) | Main | ✓ | 5 | 20.00 | 100% | 80% | 20% |
| Eastern Canada (2) | Main | ✓ | 7 | 14.29 | 86% | 57% | 0% |
| Florida | Main | ✓ | 2 | 15.00 | 100% | 50% | 0% |
| Great Lakes | Main | ✓ | 12 | 11.67 | 58% | 58% | 0% |
| Lower Mid-Atlantic | Main | ✓ | 9 | 7.78 | 78% | 0% | 0% |
| Upper Mid-Atlantic | Main | ✓ | 10 | 16.00 | 80% | 70% | 10% |
| Upper Mid-Atlantic | Main | ✓ | 2 | 15.00 | 50% | 100% | 0% |
| Midwest | Main | ✓ | 9 | 17.78 | 89% | 78% | 11% |
| North | Main | ✓ | 4 | 17.50 | 100% | 75% | 0% |
| Northeast | Main | ✓ | 11 | 16.36 | 91% | 64% | 9% |
| Pacific | Main | ✓ | 8 | 13.75 | 88% | 50% | 0% |
| South Central | Main | ✓ | 7 | 14.29 | 71% | 71% | 0% |
| Southeast | Main | ✓ | 12 | 15.00 | 83% | 58% | 8% |
| Upstate NY | Main | ✓ | 5 | 20.00 | 100% | 100% | 0% |
| UK (North) | UK | ✓ | 5 | 18.00 | 80% | 100% | 0% |
| UK (South) | UK | ✓ | 7 | 17.14 | 86% | 71% | 14% |