Source: https://guthlabs.ai/docs/instruments/uniform-circular-motion-calculator/

instrument / verified-clean

# Uniform Circular Motion Calculator

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/uniform-circular-motion-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/uniform-circular-motion-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/uniform-circular-motion-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/uniform-circular-motion-calculator/qualification/>)

## Ledger state

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

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-3

**Evidence ID**: t3-011

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## 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": {
    "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."
}
````

## Related workflows

[Kinematics & Collisions Tutorcircular](<https://guthlabs.ai/docs/instrument-workflows/kinematics-tutor/>)

## 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-tranche3/tranche3-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`