Rotational Kinematics Solver mechanism

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

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