Source: https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/mechanism/

instrument mechanism / verified-clean

# Impulse-Momentum Calculator mechanism

The inspectable method record for Impulse-Momentum Calculator, kept separate from implementation and qualification.

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

## Model scope

The listed relationships are standard under constant-mass, one-dimensional assumptions, but the specification needs clarification of force variability, vector handling, required inputs for each output, and unit normalization before it can receive PASS.

- J=FΔt is correct only when F is constant or represents the average net force over the interval; the general formula is J=∫F(t)dt.

- The formula for velocity change from force-time inputs must explicitly include Δv=J/m=FΔt/m; without mass, F and Δt alone cannot determine Δv.

- Impulse and momentum change are vectors. A scalar implementation needs an explicit one-dimensional or componentwise sign convention.

- The relation mΔv assumes constant mass. Variable-mass systems require additional treatment.

## Units and conventions

- Use net force, not an arbitrary single force, and use SI units: F in newtons, Δt in seconds, m in kilograms, Δv in meters per second, J in newton-seconds (equivalent to kg·m/s).

- F, Δv, and J are treated as signed scalar quantities along one chosen axis, or as corresponding vector components.

- The time interval Δt is a nonnegative duration.

- If alternative units are accepted, they must be converted consistently; for example, 1 kN=1000 N and 1 ms=0.001 s.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "F_N": 120,
    "delta_t_s": 0.25,
    "m_kg": 60
  },
  "expected_outputs": {
    "J_Ns": 30,
    "delta_v_m_per_s": 0.5
  },
  "working": "J=FΔt=120 N×0.25 s=30 N·s. Δv=J/m=30 kg·m/s÷60 kg=0.5 m/s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-mass input creates an undefined velocity-change result through division by zero. The sign convention is also underspecified: treating force as signed versus magnitude-only changes both impulse and velocity-change signs.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/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`