Exact normal forces and trajectories for a rotating tripod sliding on a smooth surface
Bibliographic record
Abstract
We study the motion of a rotating tripod sliding over a smooth surface. The tripod is important and unique in that it is the only case where all aspects of the motion can be solved exactly. From the three constraint equations, we calculate the three normal forces and friction forces, which we then use to calculate the trajectory and other physical quantities of interest. We report novel results: the normal force has an interesting form when the sliding speed and the speed of rotation are almost equal; the tripod can execute serpentine trajectories; trajectories can have large lateral deflections; the translational kinetic energy can decrease and increase during a full rotation; the tripod can tip at a very late stage of its motion. The tripod trajectories are compared to trajectories of rotating, sliding cylinders that have continuous contact rings. We discuss significant implications of our results. PACS No.: 45.40.–f
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".