Gyroscopic Precession Calculator

Inspectable records

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

t5-043

Ledger rows

1

No ledger note is attached.

Review findings

The honest label correctly identifies this as a steady-precession approximation that ignores nutation, but the product needs explicit assumptions or inputs for g, the torque angle, and the spin-axis moment of inertia before the formula can be presented as unambiguous.

Formula and scope findings

• mgr is only the gravitational torque magnitude when the center-of-mass displacement is perpendicular to gravity; the general magnitude is mgr sin(theta), where theta is the angle between r and g.
• Omega=tau/(I omega) is the standard steady-precession approximation only when spin angular momentum dominates, nutation is neglected, and I is the moment of inertia about the spin axis.
• The spec does not define the orientation angle, so it is ambiguous whether r means the full center-of-mass-to-pivot distance or the perpendicular lever arm.
• The gravitational acceleration g is used but is not listed as an input or fixed constant.

Unit assumptions

• Use SI units: mass in kg, r in m, I in kg*m^2, and spin omega in rad/s.
• Use g=9.80665 m/s^2 unless another value is explicitly selected.
• Omega is reported in rad/s; radians are treated as dimensionless in dimensional arithmetic.
• I must be the moment of inertia about the gyroscope's spin axis.
• The tested cases assume the center-of-mass displacement is perpendicular to gravity, so tau=mgr.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

A zero spin input produces division by zero and must be rejected. The specification also does not define a true piecewise formula branch or unambiguously define sign, unit, and directional conventions.

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": {
    "mass": 1.2,
    "r": 0.08,
    "spin_omega": 120,
    "I": 0.006,
    "units": "kg, m, rad/s, kg*m^2",
    "assumed_angle": "90 degrees",
    "g": 9.80665
  },
  "expected_outputs": {
    "Omega": 1.307553333,
    "Omega_unit": "rad/s"
  },
  "working": "tau=mgr=1.2*9.80665*0.08=0.9414384 N*m. I*omega=0.006*120=0.72 kg*m^2/s. Omega=tau/(I*omega)=0.9414384/0.72=1.307553333 rad/s."
}

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