Gyroscopic Precession Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

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