Question
Answer the following about things that make 3D special in physics, for 10 points each.
[10m] Gravitational orbits and atoms can only exist in 3D since solving the Poisson equation in 3D gives force laws with this property. Only force laws with this form and linear force laws give rise to stable orbits by Bertrand’s theorem.
ANSWER: inverse-square [accept one over r-squared or one over d-squared or one over distance-squared or one over radius-squared; prompt on central forces]
[10h] Tensor quantities like angular velocity and magnetic field can only be represented as vectors in 3D, because 2-forms and 1-forms are Hodge dual in 3D. The representations can be mapped to each other using this operator, symbolized epsilon-sub-ijk in 3D.
ANSWER: Levi-Civita symbol
[10e] The duality of vectors and rank-2 tensors explains why this operation is defined in 3D. Taking this operation of two vectors outputs a vector that is perpendicular to both.
ANSWER: cross product [prompt on vector product; reject “dot product”]
<VD, Physics>
Summary
| 2024 ARCADIA at BU | 2024-12-06 | Y | 7 | 8.57 | 57% | 29% | 0% |
| 2024 ARCADIA at Duke | 2024-12-06 | Y | 2 | 15.00 | 100% | 0% | 50% |
| 2024 ARCADIA at Missouri S&T | 2024-12-06 | Y | 2 | 25.00 | 100% | 100% | 50% |
| 2024 ARCADIA at Penn State | 2024-12-06 | Y | 2 | 25.00 | 100% | 100% | 50% |
| 2024 ARCADIA at Florida Tech | 2024-12-06 | Y | 4 | 10.00 | 75% | 25% | 0% |
| 2024 ARCADIA at UC Berkeley | 2024-12-06 | Y | 3 | 23.33 | 100% | 67% | 67% |
| 2024 ARCADIA at Waterloo | 2024-11-09 | Y | 6 | 16.67 | 100% | 33% | 33% |
| 2024 ARCADIA at GT | 2024-12-06 | Y | 5 | 10.00 | 100% | 0% | 0% |
| 2024 ARCADIA at Illinois | 2024-11-09 | Y | 4 | 20.00 | 100% | 50% | 50% |
| 2024 ARCADIA at Warwick | 2024-12-06 | Y | 5 | 24.00 | 100% | 60% | 80% |
Data
| North Carolina B | Virginia Tech B | 0 | 10 | 10 | 20 |
| Virginia Tech A | Virginia Tech C | 0 | 0 | 10 | 10 |