Newton-second

newton second
For two objects moving with the same velocity (v), the object with the greater mass (m) will have the greater momentum (p).
General information
Unit system	SI derived unit
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 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.

${\vec {F}}\cdot t=\Delta m{\vec {v}}$

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:

$\mathbf {p} =m\mathbf {v} ,$

• p is the momentum in newton second (N s) or "kilogram meters per second" (kg·m/s)
• m is the mass in kilogram
• v is the velocity in meters per second (m/s)

N s = N$\cdot$ s= kg $\cdot$ m/s

Examples

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

Mass (kg)	Speed (m/s)	Momentum newton seconds	Explanation
0.42	2.4	1	A 420 gram football (FIFA specified weight for outdoor size 5) kicked to a speed of 8.6 km/h.
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, making it one of the hardest kicks measured.
1,500	16.7	25,050	A regular small car weighing 1.5 tons crashing at 60 km/h
2,600	16.7	43,420	An SUV weighing 2.6 t (2.6 Mg) crashing at 60 km/h
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.
2,030,000	8050	1.63x1010	Space Shuttle launched from earth to orbit
45,702	10834	4.95x108	Apollo 11 launched from earth to orbit
0.0075	350	2.6	9x19 mm 7.5 gram pistol round launched at 350 m/s
0.004	945	3.8	5.56 mm (0.223) 4 gram rifle round launched at 945 m/s
0.05	860	43	12.7x99 mm (0.50 BMG) 50 gram rifle round launched at 860 m/s

See also

• Power factor
• Newton meter, the derived SI unit of torque