Newton-second | |
---|---|

General information | |

Unit system | SI derived unit |

Unit of | Impulse and momentum |

Symbol | N⋅s or N s |

Named after | Isaac Newton |

In SI base units: | kg⋅m/s |

The **newton-second** (also **newton second**; symbol: **N⋅s** or **N s**)^{[1]} is the derived SI unit of impulse. It is dimensionally equivalent to the momentum unit **kilogram-metre per second** (**kg⋅m/s**). One newton-second corresponds to a one-newton force applied for one second.

It can be used to identify the resultant velocity of a mass if a force accelerates the mass for a specific time interval.

## Definition[edit]

Momentum is given by the formula:

- is the momentum in newton-second (N⋅s) or "kilogram-metres per second" (kg⋅m/s)
- is the mass in kilogram
- is the velocity in metres per second (m/s)

## Examples[edit]

This table gives the magnitudes of some momenta for various masses and speeds.

Mass (kg) | Speed (m/s) | Momentum (N⋅s) | Explanation |
---|---|---|---|

0.42 | 2.4 | 1 | A 420-gram (15 oz) football (FIFA specified weight for outdoor size 5) kicked to a speed of 8.6 km/h (5.3 mph). |

0.42 | 38 | 16 | The momentum of the famous football kick of the Brazilian player Roberto Carlos in the match against France in 1997. The football had a speed of 137 km/h (85 mph), making it one of the hardest kicks measured. |

1300 | 10 | 13000 | A four-door car weighing 1300 kg (2900 lb) crashing at 36 km/h (22 mph). |

2000 | 10 | 20000 | A mid-size SUV weighing 2000 kg (4400 lb) crashing at 36 km/h (22 mph). |

6 | 1 | 6 | The total impulse of a class C model rocket engine, which can be found in amateur fireworks. |

10 | 2 | 20 | The total impulse of a class D model rocket engine, which also can be found in amateur fireworks. |

2030000 | 8050 | 1.63×10^{10} | Space Shuttle launched from earth to orbit |

45702 | 10834 | 4.95×10^{8} | Apollo 11 launched from earth to orbit |

0.0075 | 350 | 2.6 | A 7.5-gram (0.26 oz) handgun bullet (e.g. 9mm Parabellum) fired at 350 m/s (1100 ft/s). |

0.004 | 945 | 3.8 | A 4-gram (0.14 oz) assault rifle bullet (e.g. 5.56×45mm NATO) fired at 945 m/s (3100 ft/s). |

0.05 | 860 | 43 | A 50-gram (1.8 oz) machine gun bullet (e.g. .50 BMG) fired at 860 m/s (2800 ft/s). |

## See also[edit]

- Power factor
- Newton-metre, the derived SI unit of torque
- Orders of magnitude (momentum), for examples of momenta

## References[edit]

**^**International Bureau of Weights and Measures (2006),*The International System of Units (SI)*(PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14

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