Physics:Newton-second

Short description: SI derived unit of impulse

newton-second
For objects moving with the same velocity (v), each object's momentum (p) is proportional to its mass (m).
General information
Unit system	SI
Unit of	impulse and momentum
Symbol	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) is the unit of impulse in the International System of Units (SI). 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.

[math]\displaystyle{ \vec F \cdot t = \Delta m \vec v }[/math]

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

Definition

Momentum is given by the formula:

[math]\displaystyle{ \mathbf{p} = m \mathbf{v}, }[/math]

• [math]\displaystyle{ \mathbf{p} }[/math] is the momentum in newton-seconds (N⋅s) or "kilogram-metres per second" (kg⋅m/s)
• [math]\displaystyle{ m }[/math] is the mass in kilograms (kg)
• [math]\displaystyle{ \mathbf{v} }[/math] is the velocity in metres per second (m/s)

Examples

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.
132500	8050	1.07×109	Space Shuttle launched from Earth to orbit
45702	10834	4.95×108	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) 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) anti-material bullet (e.g. .50 BMG) fired at 860 m/s (2800 ft/s).

See also

• Power factor
• Newton-metre – SI unit of torque
• Orders of magnitude (momentum) – examples of momenta