The uncertainty of the pendulum method for the determination of the moment of inertia
Bibliographic record
Abstract
The purpose of this study was to quantify the uncertainty of the pendulum method for determining the moment of inertia of an object using various suspension distances. Experimental data were collected on a known geometric solid and partial differential equations were derived to calculate the uncertainty. Repeated measures were used to estimate the errors of the mass, period of oscillation, and distance measurements from the axis to the centre of mass. The results showed that the pendulum method was relatively insensitive to measurement errors of mass but was quite sensitive to errors in the period of oscillation. It was also found that the uncertainty of the pendulum method could be drastically reduced to less than 3% by suspending the object with the axis located at the radius of gyration. Most studies using the pendulum method to determine limb inertial properties have adopted a proximal suspension, including the often cited work by Dempster [Dempster WT. Space requirements for the seated operator. W ADC Technical Report 55-159. Ohio: Aero Medical Laboratory, Wright Air Development Centre, Air Research and Development Council, Wright-Patterson Air Force Base; 1955]. The results suggest that validation of imaging techniques to determine inertial properties should use geometric solids in addition to the pendulum method where the object is suspended at a distance estimated to be the radius of gyration. It is further recommended that the uncertainty be reported whenever it is necessary to use the pendulum method.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.012 | 0.056 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".