# Momentum Measure

A Momentum is a physical measure [math]\displaystyle{ \vec{p} }[/math] based on the multiplication of its mass [math]\displaystyle{ m }[/math] and its velocity [math]\displaystyle{ \vec{v} }[/math].

**AKA:**Linear Momentum.**Context:**

- The units of measurement of momentum are given by:

- [math]\displaystyle{ [momentum]=[mass]\times[velocity]=\frac{[mass]\times[length]}{[time]} }[/math]
- where [math]\displaystyle{ [x] }[/math] symbolizes the conversion of the quantity [math]\displaystyle{ x }[/math] to its units of measurement. Thus, the units of measurement for momentum in International System of Units this is kilograms meters per seconds, a.k.a Newton seconds (
`kg m/s`

).

- where [math]\displaystyle{ [x] }[/math] symbolizes the conversion of the quantity [math]\displaystyle{ x }[/math] to its units of measurement. Thus, the units of measurement for momentum in International System of Units this is kilograms meters per seconds, a.k.a Newton seconds (

- It can (typically) be conserved in the absence of external forces, thus it is a constant an isolated system and cannot be changed by interactions within the system.

**Example(s)**- Angular Momentum.
- Conservation of Momentum.
- The momentum of a 225 g softball moving at 35 m/s is 7.9 kg m/s.
- The momentum of a 225 g softball moving at 0 m/s is 0 kg m/s.
- …

**Counter-Example(s)****See:**Translational Symmetry, Pool (Cue Sports), Classical Mechanics, Plural, SI, Kilogram, Meters Per Second, Newton Second, Mass, Velocity, Euclidean Vector, Closed System.

## References

### 2016

- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/momentum Retrieved:2016-4-29.
- In classical mechanics,
**linear momentum**or**translational momentum**(pl. momenta; SI unit kg m/s, or equivalently, newton second) is the product of the mass and velocity of an object. For example, a heavy truck moving rapidly has a large momentum — it takes a large or prolonged force to get the truck up to this speed, and it takes a large or prolonged force to bring it to a stop afterwards. If the truck were lighter, or moving more slowly, then it would have less momentum.Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude: : [math]\displaystyle{ \mathbf{p} = m \mathbf{v}, }[/math] where

**p**is the three-dimensional vector stating the object's momentum in the three directions of three-dimensional space,**v**is the three-dimensional velocity vector giving the object's rate of movement in each direction, and*m*is the object's mass.Linear momentum is also a

*conserved*quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change.In classical mechanics, conservation of linear momentum is implied by Newton's laws. It also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is ultimately an expression of one of the fundamental symmetries of space and time, that of translational symmetry.

- In classical mechanics,

### 2005

- (Hyperphysics Encyclopedia, 2005) ⇒ http://hyperphysics.phy-astr.gsu.edu/hbase/mom.html#mom
- QUOTE: The momentum of a particle is defined as the product of its mass times its velocity. It is a vector quantity. The momentum of a system is the vector sum of the momenta of the objects which make up the system. If the system is an isolated system, then the momentum of the system is a constant of the motion and subject to the principle of conservation of momentum.

- The basic definition of momentum applies even at relativistic velocities but then the mass is taken to be the relativistic mass.
- The most common symbol for momentum is p. The SI unit for momentum is kg m/s.

- [math]\displaystyle{ \vec{p}=m*\vec{v} }[/math]
- You may insert numbers for any of the quantities. Then click on the text or symbol in the formula above for the quantity you wish to calculate. The numbers will not be forced to be consistent until you click on the desired quantity.

### 2005

- (Wolfram Science World, 2005) ⇒ http://scienceworld.wolfram.com/physics/Momentum.html
- QUOTE: Momentum is a fundamental quantity in mechanics that is conserved in the absence of external forces. Conservation of momentum follows from invariance under translation by Noether's symmetry theorem. Eric Weisstein's World of Math A similar quantity conserved in the absence of noncentral forces is called angular momentum.

- For a single particle of mass m with velocity [math]\displaystyle{ \vec{v} }[/math], the momentum is defined as

- [math]\displaystyle{ \vec{p}=m\vec{v}=m\;\frac{d\vec{r}}{dt} }[/math]
- From Newton's second law, a force [math]\displaystyle{ \vec{F} }[/math] produces a change in momentum

- [math]\displaystyle{ \vec{F}=m\;\frac{d\vec{p}}{dt} }[/math]
- Therefore, if [math]\displaystyle{ \vec{F}=0 }[/math], then

- [math]\displaystyle{ \frac{d\vec{p}}{dt}=0 }[/math]
- and [math]\displaystyle{ \vec{p}=constant }[/math] so the particle has constant velocity.

### 1963

- (Feynman et al., 1963) ⇒ Richard P. Feynman, Robert B. Leighton and Matthew Sands (1963, 1977, 2006, 2010, 2013) "The Feynman Lectures on Physics": New Millennium Edition is now available online by the California Institute of Technology, Michael A. Gottlieb, and Rudolf Pfeiffer ⇒ http://www.feynmanlectures.caltech.edu/
- See: Chapter 10 ⇒ http://www.feynmanlectures.caltech.edu/I_10.html