Uniform Circular Motion Calculator mechanism

Model scope

The centripetal acceleration, force, and period formulas are standard under the stated SI assumptions. Approval requires adding the frequency formula, defining signed-versus-unsigned speed/angular velocity behavior, specifying zero and invalid-radius handling, and clearly labeling that force requires mass.

• The output list includes frequency f, but no formula is specified; it should explicitly define f=1/T=v/(2πr)=|ω|/(2π).
• The input choice 'v or ω' is underspecified: when ω is supplied, the instrument must use v=|ω|r or calculate T=2π/|ω| directly, and it must define whether signed ω is accepted.
• F_c=ma_c is correct only when m is supplied and F_c means the net inward radial force; the specification should state that mass is required for the force output.

Units and conventions

• Use SI units unless unit conversion is explicitly supported: v in m/s, r in m, m in kg, a_c in m/s², F_c in N, T in s, and f in Hz.
• ω is in rad/s; radians are dimensionless for arithmetic, and one complete revolution is 2π radians.
• r must be positive for a nondegenerate circular path.
• v is tangential speed and is treated as nonnegative; if signed velocity is accepted, the formulas should use its magnitude.
• For a supplied ω, v and ω must satisfy v=|ω|r if both are provided.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "v": 10,
    "v_unit": "m/s",
    "r": 5,
    "r_unit": "m",
    "mass": 2,
    "mass_unit": "kg"
  },
  "expected_outputs": {
    "a_c": 20,
    "a_c_unit": "m/s^2",
    "F_c": 40,
    "F_c_unit": "N",
    "T": 3.1415926536,
    "T_unit": "s",
    "f": 0.3183098862,
    "f_unit": "Hz"
  },
  "working": "a_c=v²/r=10²/5=100/5=20 m/s². F_c=ma_c=2×20=40 N. T=2πr/v=2×π×5/10=π=3.1415926536 s. f=1/T=1/π=0.3183098862 Hz."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification does not state validation for r=0, which makes a_c and F_c undefined and represents an invalid circular-motion state. It also does not define whether a signed v is treated as a directional velocity or as a nonnegative speed for T and f.

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-tranche3/tranche3-results.json
• BOUNDARY_HAZARD_CATALOG.json