Question
To obtain the equations of motion for this device, the z direction is ignored, and then a complex number is introduced to solve the coupled differential equations for x and y. For 10 points each:
[10m] Name this device whose plane of oscillation has an angular velocity equal to the Earth’s angular velocity times the cosine of colatitude.
ANSWER: Foucault (“foo-koh”) pendulum [or Foucault’s pendulum] (It is named after Léon Foucault.)
[10e] The forces on the Foucault pendulum include this fictitious force that deflects objects rightward in the Northern Hemisphere.
ANSWER: Coriolis force
[10h] This operation can be used to explain the rotation of the plane of oscillation. Given del as the covariant derivative induced by a connection between the tangent bundle of a manifold and the manifold, this operation moves a vector field X along a smooth curve while keeping “del X” equal to zero.
ANSWER: parallel transport
<Physics>
Summary
| 2023 ACF Nationals | 04/22/2023 | Y | 21 | 15.24 | 91% | 43% | 19% |
Data
| Columbia A | UC Berkeley B | 10 | 10 | 10 | 30 |
| Columbia B | Indiana A | 10 | 10 | 10 | 30 |
| NYU A | Cornell B | 0 | 10 | 0 | 10 |
| Duke A | Chicago C | 0 | 10 | 0 | 10 |
| Imperial A | UC Berkeley A | 0 | 10 | 0 | 10 |
| Michigan A | Illinois A | 0 | 0 | 0 | 0 |
| Minnesota B | Georgia Tech B | 10 | 10 | 0 | 20 |
| Penn A | Chicago A | 0 | 0 | 0 | 0 |
| Vanderbilt A | Rutgers A | 0 | 10 | 0 | 10 |
| WUSTL B | Texas A | 0 | 10 | 0 | 10 |
| Purdue A | Yale B | 0 | 10 | 0 | 10 |
| Chicago B | Johns Hopkins A | 0 | 10 | 0 | 10 |
| Florida A | Toronto A | 0 | 10 | 10 | 20 |
| South Carolina A | WUSTL A | 0 | 10 | 0 | 10 |
| Ohio State A | Yale A | 10 | 10 | 0 | 20 |
| Georgia Tech A | MIT A | 10 | 10 | 0 | 20 |
| Minnesota A | Houston A | 10 | 10 | 0 | 20 |
| Iowa State A | North Carolina A | 0 | 10 | 10 | 20 |
| Brown A | Northwestern A | 10 | 10 | 0 | 20 |
| Virginia A | Cornell A | 10 | 10 | 0 | 20 |
| Maryland A | Harvard A | 10 | 10 | 0 | 20 |