Source: https://guthlabs.ai/docs/instruments/rotational-kinematics-solver/mechanism/

instrument mechanism / verified-clean

# Rotational Kinematics Solver mechanism

The inspectable method record for Rotational Kinematics Solver, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The equations themselves are correct for one-dimensional rotation with constant angular acceleration, but the advertised 'any 3' input capability needs an explicit solvability and branch-selection policy. The honest_label value 'n/a' does not disclose the constant-acceleration assumption, required radians, sign conventions, or failure modes.

- All three equations are standard constant-angular-acceleration equations, but the specification does not state that α must be constant.

- The claim that any 3 of {ω0, ω, α, t, θ} always determine the remaining unknowns is ambiguous and not universally true: some combinations produce multiple real solutions, no real solution, or degenerate equations.

- Solving ω²=ω0²+2αθ for ω or ω0 requires a sign choice; the squared equation alone cannot determine the direction of rotation.

- The specification does not define how inconsistent inputs, multiple solutions, or negative radicands are reported.

## Units and conventions

- ω0 and ω are signed angular velocities in radians per second (rad/s).

- α is signed constant angular acceleration in radians per second squared (rad/s²).

- θ is signed angular displacement in radians; degrees must be converted to radians before use.

- t is elapsed time in seconds and is normally constrained to t≥0.

- All inputs must use a consistent rotation sign convention.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "omega0": 2,
    "alpha": 3,
    "t": 4
  },
  "expected_outputs": {
    "omega": 14,
    "theta": 32
  },
  "working": "ω = ω0 + αt = 2 + 3×4 = 14 rad/s. θ = ω0t + ½αt² = 2×4 + ½×3×4² = 8 + 1.5×16 = 8 + 24 = 32 rad. Consistency check: ω² = 14² = 196; ω0² + 2αθ = 2² + 2×3×32 = 4 + 192 = 196."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The solver has a genuine undefined-result failure when alpha=0 and omega=omega0: time is 0/0 and theta is non-unique. It also has a branch-selection hazard because a valid input set can produce two nonnegative times and two angular velocities.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/rotational-kinematics-solver/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/rotational-kinematics-solver/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/rotational-kinematics-solver/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`