Source: https://guthlabs.ai/docs/instruments/rotational-kinetic-energy-calculator/

instrument / verified-clean

# Rotational Kinetic Energy 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](<https://guthlabs.ai/docs/instruments/rotational-kinetic-energy-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/rotational-kinetic-energy-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/rotational-kinetic-energy-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/rotational-kinetic-energy-calculator/qualification/>)

## 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-5

**Evidence ID**: t5-032

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The rotational formula passes standard physics checks, but the specification needs explicit axis, unit, and rolling-condition assumptions. Test vector 2 intentionally demonstrates that the declared rolling input set m,v,I is insufficient for the stated total-energy formula without ω or a radius/constraint. The honest_label value n/a should be replaced with a user-facing limitations label describing these assumptions.

### Formula and scope findings

- The formulas are standard and correct when I is the moment of inertia about the rotating body's center of mass, ω is angular speed in rad/s, and v is center-of-mass speed in m/s.

- For the rolling claim, the specification does not state whether rolling without slipping is required. If so, it must state and optionally validate v=Rω.

- The rolling expression is valid as a translation-plus-rotation decomposition only when I is about the center of mass; using I about another axis, such as the contact point, would make the expression ambiguous or incorrect.

- The output name KE_rot is ambiguous for rolling inputs: it should distinguish rotational energy from total kinetic energy, and may optionally expose the translational component separately.

### Unit assumptions

- I is in kg·m².

- ω is in rad/s; revolutions per second or rpm must be converted before squaring.

- m is in kg.

- v is the center-of-mass speed in m/s.

- Outputs are in joules, since 1 kg·m²/s² = 1 J.

- For rolling without slipping, v and ω must satisfy v=Rω with R in meters.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

Plain JavaScript arithmetic overflows to Infinity for sufficiently large finite inputs, and the specification leaves the rolling input set and angular-speed unit convention under-specified.

## 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": {
    "I_kg_m2": 2.4,
    "omega_rad_s": 5
  },
  "expected_outputs": {
    "KE_rot_J": 30
  },
  "working": "KE_rot = ½Iω² = ½(2.4)(5.0²) = 1.2×25 = 30 J."
}
````

## 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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`