Rotational Kinematics & Moment of Inertia (Rigid Bodies)

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

Tranche

tranche-6

Evidence ID

t6-093

Ledger rows

1

No ledger note is attached.

Review findings

No listed numerical formula is inherently incorrect, but the exact validity conditions and units are underspecified. Verdict is NEEDS_REVIEW because the shape-axis/material assumptions, constant-acceleration condition, unit contract, and treatment of α as an output are ambiguous.

Formula and scope findings

• The angular kinematics formulas are correct only when angular acceleration α is constant over the interval: ω=ω0+αt and θ=ω0t+0.5αt².
• I_disk=0.5mr² is valid for a uniform, solid, thin disk about its central axis perpendicular to the disk.
• I_rod(center)=mL²/12 is valid for a uniform, slender rod about an axis through its center and perpendicular to its length.
• I_sphere=0.4mr² is valid for a uniform solid sphere about any diameter; a hollow sphere requires a different formula.
• I_hoop=mr² is valid for a thin hoop/ring about its central symmetry axis.
• The spec lists α as an output, but supplies no formula for determining α from other quantities; α must be an input or an additional inverse formula must be specified.

Unit assumptions

• Use one consistent unit system: mass in kg, length in m, time in s, angular velocity in rad/s, angular acceleration in rad/s², and angular displacement in radians.
• The radius must be supplied directly or computed from a diameter using r=D/2; unit conversion must occur before applying moment-of-inertia formulas.
• Radians are dimensionless in the arithmetic, but angular quantities should still be labeled in radians for clarity.
• Mass and all geometric dimensions must be nonnegative; t is normally nonnegative unless reverse-time evaluation is explicitly allowed.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The extreme disk input produces a mathematical moment of inertia of 5e615 kg m^2, which overflows ordinary JavaScript Number arithmetic to Infinity. The instrument should reject or explicitly flag this out-of-range input rather than silently returning a non-finite value.

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": {
    "kinematics": {
      "omega0": 5,
      "alpha": -2,
      "t": 0,
      "units": {
        "omega0": "rad/s",
        "alpha": "rad/s^2",
        "t": "s"
      }
    },
    "inertia": {
      "shape": "thin hoop",
      "mass": 2,
      "radius": 0.3,
      "units": {
        "mass": "kg",
        "radius": "m"
      }
    }
  },
  "expected_outputs": {
    "omega": "5.00000 rad/s",
    "theta": "0 rad",
    "I": "0.180000 kg·m²"
  },
  "working": "Kinematics at the zero-time boundary: ω=ω0+αt=5+(-2)(0)=5 rad/s. θ=ω0t+0.5αt²=(5)(0)+0.5(-2)(0²)=0 rad. Hoop inertia: I=mr²=(2)(0.3²)=(2)(0.09)=0.18 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