Source: https://guthlabs.ai/docs/instruments/moment-of-inertia-lookup-calculator/
instrument / verified-clean
# Moment of Inertia Lookup & Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo
**Tranche**: tranche-6
**Evidence ID**: t6-027
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The listed equations are correct textbook results under the stated idealizations. The instrument should expose the standard axis for every shape, explicitly label the sphere as solid or hollow, define accepted units and conversions, and validate the parallel-axis geometry before it can be approved.
### Formula and scope findings
- The formulas are standard only for specific idealized bodies and axes: the disk formula is for a uniform thin disk about its central axis perpendicular to its face; the rod formula is for a uniform slender rod about an axis through its center perpendicular to its length; the sphere formula is for a uniform solid sphere about any diameter; and the hoop formula is for a thin hoop about its central axis.
- The shape specification does not distinguish a solid sphere from a hollow spherical shell, nor a thin disk from a solid cylinder, so the shape-to-formula mapping is ambiguous.
- The parallel-axis theorem requires the two axes to be parallel and separated by perpendicular distance d; this constraint should be stated and enforced.
- The input specification does not define the reference axis for each shape or whether dimensions describe thin bodies, solid bodies, or shells.
### Unit assumptions
- M is in kilograms, all lengths including R, L, and d are in metres, and the output I is in kg·m².
- The disk is uniform and thin, with its axis perpendicular to the disk through its center.
- The rod is uniform and slender, with the reference axis perpendicular to the rod through its center.
- The sphere is a uniform solid sphere, with the reference axis through its center.
- The hoop is a uniform thin hoop, with the reference axis through its center perpendicular to its plane.
- For the parallel-axis calculation, d is the perpendicular separation between parallel axes.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The extreme-magnitude disk input produces Infinity in ordinary IEEE-754 JavaScript arithmetic. Without finite-value validation or an overflow warning, the calculator can return a nonphysical non-finite result.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"shape": "uniform thin disk",
"M_kg": 2.4,
"R_m": 0.5,
"d_m": 0.3,
"axis": "parallel to central symmetry axis, offset by d"
},
"expected_outputs": {
"I_cm_kg_m2": 0.3,
"I_about_offset_axis_kg_m2": 0.516
},
"working": "I_cm = 1/2 MR² = 1/2 × 2.4 × (0.5)² = 1.2 × 0.25 = 0.300 kg·m². Md² = 2.4 × (0.3)² = 2.4 × 0.09 = 0.216 kg·m². I = I_cm + Md² = 0.300 + 0.216 = 0.516 kg·m²."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche6/tranche6-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`