Rotational Kinetic Energy Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json