Source: https://guthlabs.ai/docs/instruments/rotational-kinematics-moment-of-inertia-rigid-bodies/

instrument / verified-clean

# Rotational Kinematics & Moment of Inertia (Rigid Bodies)

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-kinematics-moment-of-inertia-rigid-bodies/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/rotational-kinematics-moment-of-inertia-rigid-bodies/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/rotational-kinematics-moment-of-inertia-rigid-bodies/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/rotational-kinematics-moment-of-inertia-rigid-bodies/qualification/>)

## 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`