# Momentum Calculator

> Computes linear momentum from mass and velocity, the matching kinetic energy, and, when a stopping time is given, the average force needed to bring the object to rest (impulse–momentum theorem).

- Calculator id: `momentum` · Category: Physics (`physics`) · Tool name: `calculate_momentum`
- Canonical page: https://tttkmbb.com/physics/momentum · This document: https://tttkmbb.com/physics/momentum.md · JSON definition: https://tttkmbb.com/physics/momentum.json

## Purpose

Computes linear momentum from mass and velocity, the matching kinetic energy, and, when a stopping time is given, the average force needed to bring the object to rest (impulse–momentum theorem).

**Use when:** You need an object's momentum, or the average force involved in stopping or launching it over a known time (collisions, braking, catching a ball).

**Do not use when:** You need the outcome of a two-body collision (conservation of momentum between two objects is not implemented), or only the energy of motion (use kinetic-energy).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `mass_kg` | number | kg | required | Mass of the object in kilograms. (> 0) |
| `velocity_m_s` | number | m/s | required | Velocity in metres per second; sign indicates direction along the line of motion. |
| `stop_time_s` | number | s | optional | Optional time over which the object is brought to rest; enables the average force output. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `momentum_kg_m_s` | number | kg·m/s | p = m × v (same sign as the velocity). |
| `kinetic_energy_j` | number | J | ½ × m × v² for the same object. |
| `average_stopping_force_n` | number | N | \|p\| / stop_time_s: mean force to remove all momentum in the given time (only when stop_time_s is given). |

## Formula

`p = mass_kg × velocity_m_s; KE = ½ × mass_kg × velocity_m_s²; average_stopping_force_n = |p| / stop_time_s (impulse F·Δt = Δp)`

## Data Sources

- HyperPhysics – Momentum — http://hyperphysics.phy-astr.gsu.edu/hbase/mom.html (reference, retrieved 2026-09-23)
- Wikipedia – Momentum — https://en.wikipedia.org/wiki/Momentum (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/momentum?mass_kg=…&velocity_m_s=…`
- `POST https://tttkmbb.com/api/v1/calculate/momentum` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/momentum · OpenAPI operationId `calculate_momentum` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "momentum", "inputs": {…}}`

## Example

- 1200 kg car at 25 m/s stopped in 3 s: inputs `{"mass_kg":1200,"velocity_m_s":25,"stop_time_s":3}` → `{"momentum_kg_m_s":30000,"kinetic_energy_j":375000,"average_stopping_force_n":10000}`
- 57 g tennis ball at 50 m/s: inputs `{"mass_kg":0.057,"velocity_m_s":50}` → `{"momentum_kg_m_s":2.85,"kinetic_energy_j":71.25}`

```
GET https://tttkmbb.com/api/v1/calculate/momentum?mass_kg=1200&velocity_m_s=25&stop_time_s=3
```

## Limitations

You need the outcome of a two-body collision (conservation of momentum between two objects is not implemented), or only the energy of motion (use kinetic-energy). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What is the unit of momentum?**

Kilogram-metres per second (kg·m/s), equivalent to newton-seconds (N·s), the unit of impulse.

**Why does a longer stopping time reduce the force?**

The impulse (force × time) needed equals the momentum change, so spreading it over more time (crumple zones, airbags, bending the knees) lowers the average force.

## Related

- [Kinetic Energy Calculator](https://tttkmbb.com/physics/kinetic-energy.md) — Energy of the same moving object.
- [Force Calculator](https://tttkmbb.com/physics/newtons-second-law.md) — Force from mass and acceleration.