# Encyclopedia

Classical mechanics $\mathbf{F} = \frac{\mathrm{d}}{\mathrm{d}t}(m \mathbf{v})$
Newton's Second Law
History of ...
Fundamental concepts
Space · Time · Mass · Force
Energy · Momentum
 Momentum Expressed in (SI unit): kg · m/s Commonly used symbols: p Conserved: yes Expressed in other quantities: p = mv p = γm0v  Title page of the 1st edition of Isaac Newton's Principia defining the laws of motion.
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In classical mechanics, momentum (pl. momenta; SI unit kg·m/s, or, equivalently, N·s) is the product of the mass and velocity of an object (p = mv).
^ The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

^ IP, G., Market Mass Times Velocity= Momentum.

^ In each of these examples, a mass unit is multiplied by a velocity unit to provide a momentum unit.

In relativistic mechanics, this quantity is multiplied by the Lorentz factor. .Momentum is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum.^ Login Copy & paste this link to your blog or website to reference this page Related Searches Physics momentum Law of conservation...
• Momentum Synonym | Synonym of Momentum and Antonym of Momentum at Thesaurus.com 9 January 2010 19:38 UTC thesaurus.reference.com [Source type: Reference]
• Momentum Definition | Definition of Momentum at Dictionary.com 9 January 2010 19:38 UTC dictionary.reference.com [Source type: Reference]

^ Definition and Pronunciation conservation of linear momentum: meaning and definitions - conservation of linear momentum: Definition and Pronunciation conservation of angular momentum: meaning and definitions - conservation of angular momentum: Definition and Pronunciation momentum: meaning and definitions - momentum: Definition and Pronunciation orbital angular momentum: meaning and definitions - orbital angular momentum: Definition and Pronunciation See more Encyclopedia articles on: Physics Premium Partner Content Related content from HighBeam Research on: momentum .
• http://www.infoplease.com/ce6/sci/A0833663.html 9 January 2010 19:38 UTC www.infoplease.com [Source type: Academic]

^ However, both linear and angular momentum is always conserved when no external force and torque act on the system.

.Linear momentum is a vector quantity, since it has a direction as well as a magnitude.^ It is a vector quantity, since it is the difference of two vector quantities.

^ Yes, momentum is a vector quantity.

^ Momentum is a vector quantity described by both direction and magnitude.

.Angular momentum is a pseudovector quantity because it gains an additional sign flip under an improper rotation.^ For a rigid body, angular momentum is also the ordinary product of moment of inertia (a scalar) and angular velocity (a pseudovector).

^ The Earth has to gain the same momentum as the ball but because the mass of the Earth is so large, the movement is unmeasurable.
• Momentum 9 January 2010 19:38 UTC www.splung.com [Source type: Academic]

.The total momentum of any group of objects remains the same unless outside forces act on the objects (law of conservation of momentum).^ Force impressed on an object will change its momentum 3.3.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ If a force acts in the same direction as the object's motion, then the force speeds the object up.

^ Momentum is a conserved quantity (it remains constant unless acted upon by an outside force), and is related by Noether's theorem to translational invariance .
• Momentum Definition | Definition of Momentum at Dictionary.com 9 January 2010 19:38 UTC dictionary.reference.com [Source type: Reference]

.Momentum is a conserved quantity, meaning that the total momentum of any closed system (one not affected by external forces) cannot change.^ Force impressed on an object will change its momentum 3.3.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ Law of conservation of momentum A closed system, is a system in which no external force applies.

^ Therefore, the total momentum change is zero.
• Momentum 9 January 2010 19:38 UTC www.splung.com [Source type: Academic]

.Although originally seen to be due to Newton's laws, this law is also true in special relativity, and with appropriate definitions a (generalized) momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.^ However, it turns out that conservation of momentum can be deduced from Newton ’s laws.

^ Newton originally stated second law in terms of momentum: .
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ Explain how conservation of momentum follows logically from Newton's laws .
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

## History of the concept

.Mōmentum was not merely the motion, which was mōtus, but was the power residing in a moving object, captured by today's mathematical definitions.^ If an object is in motion ( on the move ) then it has momentum.

^ Cite This Source Word Origin & History momentum 1699, "quantity of motion of a moving body," from L. momentum "movement, moving power" (see moment ).
• Momentum Definition | Definition of Momentum at Dictionary.com 9 January 2010 19:38 UTC dictionary.reference.com [Source type: Reference]

^ All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.

A mōtus, "movement", was a stage in any sort of change, while velocitas, "swiftness", captured only speed. .The concept of momentum in classical mechanics was originated by a number of great thinkers and experimentalists.^ In classical mechanics, momentum is defined as mass times velocity.
• Momentum Definition | Definition of Momentum at Dictionary.com 9 January 2010 19:38 UTC dictionary.reference.com [Source type: Reference]

^ Note to the teacher Momentum is a fundamental concept in Newtonian mechanics, but in the original version of "Stargazers" it was left out, in the interest of brevity.

.The first of these was Ibn Sina (Avicenna) circa 1000, during the Islamic Renaissance who referred to impetus as proportional to the mass times the velocity.^ Momentum defined: mass times velocity .
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ Momentum is mass times velocity.

^ The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.


.René Descartes believed that the total "quantity of motion" in the universe is conserved, where the quantity of motion is understood as the product of size and speed.^ Considerations and experiments like this led Descartes to invent the concept of “momentum”, meaning “amount of motion”, and to state that for a moving body the momentum was just the product of the mass of the body and its speed.

.This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more importantly he believed that it is speed rather than velocity that is conserved.^ See also conservation law ; angular momentum .
• momentum (physics) -- Britannica Online Encyclopedia 9 January 2010 19:38 UTC www.britannica.com [Source type: Academic]

^ This is true since momentum change = mass  velocity change.

^ Laws of conservation of momentum?
• WikiAnswers - What is momentum 9 January 2010 19:38 UTC wiki.answers.com [Source type: General]

.So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion.^ PDF Problem 3 Motion of a ball falling and bouncing off of the ground.
• Free Online MIT Course Materials for High School | AP Physics | Systems of Particles, Linear Momentum | Impulse and Momentum | MIT OpenCourseWare 9 January 2010 19:38 UTC ocw.mit.edu [Source type: Academic]

^ After the catch, there is a total mass of 50kg moving at a speed of 0.5 meters per second, so the final momentum is 0.5x50 = 25, the total final amount is equal to the total initial amount.

^ Similarly, for two objects of the same mass moving in the same direction at different velocities, the object traveling at the higher velocity has more momentum.

 Galileo, later, in his Two New Sciences, used the Italian word "impeto."
The question has been much debated as to what Isaac Newton contributed to the concept. .The answer is apparently nothing, except to state more fully and with better mathematics what was already known.^ Every year, the theatre’s line up is better and better with innovative renditions of classic Shakespearean plays to more contemporary shows by well known play writes.

.Yet for scientists, this was the death knell for Aristotelian physics and supported other progressive scientific theories (i.e., Kepler's laws of planetary motion).^ According to Newton's second law of motion—named after English scientist Sir Isaac Newton—a force acting on an object in motion is equal to the rate of change of momentum over time.

^ The error that finds the body not fully supported over one foot or the other will become part of your physical memory.

.Conceptually, the first and second of Newton's Laws of Motion had already been stated by John Wallis in his 1670 work, Mechanica sive De Motu, Tractatus Geometricus: "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result". Wallis uses momentum and vis for force.^ Newton's second law Moment Of Inertia Moment .

^ Isaac Newton ’s second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.
• momentum (physics) -- Britannica Online Encyclopedia 9 January 2010 19:38 UTC www.britannica.com [Source type: Academic]

^ See Newton’s laws of motion .
• momentum (physics) -- Britannica Online Encyclopedia 9 January 2010 19:38 UTC www.britannica.com [Source type: Academic]

.Newton's Philosophiæ Naturalis Principia Mathematica, when it was first published in 1686, showed a similar casting around for words to use for the mathematical momentum.^ At first glance, investing in momentum stocks using a trading system sure looks like a dumb idea .

^ One useful consequence of Newton's 3rd law is the conservation of momentum, as is shown by analyzing the recoil of a cannon.

^ Thus, a momentum trader essentially uses momentum indicators to trade possible breakouts in futures or futures options , which are showing momentum according to the trading system on the charts.

.His Definition II defines quantitas motus, "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum.^ When momentum is defined this way, as Newton defined it, "the quantity of motion", it becomes apparent that the force required to stop a moving mass depends on its momentum, not on the mass or the velocity alone.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ Since the momentum depends on the velocity, it is also a vector quantity.
• Momentum 9 January 2010 19:38 UTC www.splung.com [Source type: Academic]

^ There is however a problem here—obviously one can imagine collisions in which the “total amount of motion”, as defined above, is definitely not the same before and after.

 .Thus when in Law II he refers to mutatio motus, "change of motion", being proportional to the force impressed, he is generally taken to mean momentum and not motion.^ Force impressed on an object will change its momentum 3.3.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ Isaac Newton ’s second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.
• momentum (physics) -- Britannica Online Encyclopedia 9 January 2010 19:38 UTC www.britannica.com [Source type: Academic]

^ An examination of rows 1 and 3 show that mass and force are directly proportional; for the same time and velocity change, a fivefold increase in the mass corresponds to a fivefold increase in the force required to stop that mass.

 .It remained only to assign a standard term to the quantity of motion.^ We assign reference terms to each statement within a standards document and to each media resource, and correlations are based upon matches of these terms for a given grade band.

.The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jenning's Miscellanea in 1721, four years before the final edition of Newton's Principia Mathematica, momentum M or "quantity of motion" was being defined for students as "a rectangle", the product of Q and V where Q is "quantity of material" and V is "velocity", s/t.^ Define conservation of momentum and use it in an example.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ When momentum is defined this way, as Newton defined it, "the quantity of motion", it becomes apparent that the force required to stop a moving mass depends on its momentum, not on the mass or the velocity alone.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ At first glance, investing in momentum stocks using a trading system sure looks like a dumb idea .


Some languages, such as French and Italian, still lack a single term for momentum, and use a phrase such as the literal translation of "quantity of motion".

## Linear momentum of a particle  Newton's apple in Einstein's elevator, a frame of reference. In it the apple has no velocity or momentum; outside, it does.
.If an object is moving in any reference frame, then it has momentum in that frame.^ Momentum is usually represented by the letter p : p = m v Since velocity depends on reference frames, all magnitudes must include the reference frame .
• momentum@Everything2.com 9 January 2010 19:38 UTC www.everything2.com [Source type: FILTERED WITH BAYES]

^ Similarly, for two objects of the same mass moving in the same direction at different velocities, the object traveling at the higher velocity has more momentum.

^ In other words, for two objects of different masses moving at the same velocity, the more massive object has more momentum.

.It is important to note that momentum is frame dependent.^ Learn how trend and momentum determines the rite time frame at those all important market turns.
• Forex MomentumTrend Trading System 9 January 2010 19:38 UTC www.momentumtrend.com [Source type: General]

.That is, the same object may have a certain momentum in one frame of reference, but a different amount in another frame.^ The total amount of momentum in a closed system remains constant, but may be transferred from one object to another.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ For the equations of the conservation of momentum, the units are not important, as long as the same ones are used before and after the collision (i.e.

^ As soon as this order is executed, the disciplined momentum trader immediately places a stop order limiting his loss to a certain fixed amount, which is determined by his trading system.

.For example, a moving object has momentum in a reference frame fixed to a spot on the ground, while at the same time having 0 momentum in a reference frame attached to the object's center of mass.^ How to Gauge momentum in each time frame.
• Forex MomentumTrend Trading System 9 January 2010 19:38 UTC www.momentumtrend.com [Source type: General]

^ Momentum defined: mass times velocity .
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ Momentum is mass times velocity.

.The amount of momentum that an object has depends on two physical quantities: the mass and the velocity of the moving object in the frame of reference.^ What is the momentum P of a mass m moving with velocity v?

^ Momentum is defined as the mass multiplied by the velocity.
• Momentum 9 January 2010 19:38 UTC www.splung.com [Source type: Academic]

^ Now, the momentum is mv , mass x velocity.

In physics, the usual symbol for momentum is a bold p (bold because it is a vector); so this can be written $\mathbf{p}= m \mathbf{v}\,\!$
where .p is the momentum, m is the mass and v is the velocity.^ What is the momentum P of a mass m moving with velocity v?

^ Momentum is the product between mass and velocity .

^ Now, the momentum is mv , mass x velocity.

.Example: a model airplane of 1 kg traveling due north at 1 m/s in straight and level flight has a momentum of 1 kg m/s due north measured from the ground.^ For example, do individuals with higher levels of mental toughness perceive more examples of positive psychological momentum and less negative momentum than their less tough counterparts?
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

^ Momentum Webcast: Charting Your Path on the SAM Maturity Model (Level 100) .
• Momentum: Drive Your Midsize Business Forward 9 January 2010 19:38 UTC www.microsoft.com [Source type: General]

^ Momentum Webcast: Save Money and Travel with Integrated and Interoperable Communications (Level 100) .
• Momentum: Drive Your Midsize Business Forward 9 January 2010 19:38 UTC www.microsoft.com [Source type: General]

.To the dummy pilot in the cockpit it has a velocity and momentum of zero.^ It will accelerate , thus increasing its momentum, and then reach a velocity of zero , reducing its momentum to zero.
• momentum@Everything2.com 9 January 2010 19:38 UTC www.everything2.com [Source type: FILTERED WITH BAYES]

.According to Newton's second law, the rate of change of the momentum of a particle is proportional to the resultant force acting on the particle and is in the direction of that force.^ Force impressed on an object will change its momentum 3.3.
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ The original second law , paraphrased, is: The rate of change of momentum of a body is proportional to the net force applied to it.
• momentum@Everything2.com 9 January 2010 19:38 UTC www.everything2.com [Source type: FILTERED WITH BAYES]

^ Newton's second law Moment Of Inertia Moment .

.The derivation of force from momentum is given below, however because mass is constant the second term of the derivative is 0 so it is ignored.^ A depends on its mass for a given amount of momentum .
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

^ If a 5-kg object experiences a 10-N force for a duration of 0.10-second, then what is the momentum change of the object?

^ To understand how this comes about, consider first Newton ’s Second Law relating the acceleration a of a body of mass m with an external force F acting on it: . $\sum{\mathbf{F}} = {\mathrm{d}\mathbf{p} \over \mathrm{d}t} = m{\mathrm{d}\mathbf{v} \over \mathrm{d}t} + v{\mathrm{d}\mathbf{m} \over \mathrm{d}t} = m\mathbf{a} \,\!$
or just simply $\mathbf{F}= m \mathbf{a}\,\!$
where F is understood to be the resultant.
Example: a model airplane of 1 kg accelerates from rest to a velocity of 1 m/s due north in 1 s. The thrust required to produce this acceleration is 1 newton. .The change in momentum is 1 kg m/s.^ This impulse would cause a momentum change of 720 kgm/s.

^ If a 5-kg object experiences a 10-N force for a duration of 0.10-second, then what is the momentum change of the object?

.To the dummy pilot in the cockpit there is no change of momentum.^ When force is zero, there is no change in momentum.

^ Title changed to "momentum" from "momentum (non-relativistic)", because that was getting no autolinking at all.

^ In the case of angular momentum, when no external Torque is applied on a system, there is no change in angular momentum.

Its pressing backward in the seat is a reaction to the unbalanced thrust, shortly to be balanced by the drag.

## Linear momentum of a system of particles

### Relating to mass and velocity

The linear momentum of a system of particles is the vector sum of the momenta of all the individual objects in the system: $\mathbf{P}= \sum_{i = 1}^n m_i \mathbf{v}_i = m_1 \mathbf{v}_1 + m_2 \mathbf{v}_2 + m_3 \mathbf{v}_3 + \cdots + m_n \mathbf{v}_n \,\!$
where .P is the total momentum of the particle system, mi and vi are the mass and the velocity vector of the i-th object, and n is the number of objects in the system.^ Now, the momentum is mv , mass x velocity.

^ And if the velocity of the object is changed, then the momentum of the object is changed.

^ Momentum and system of particles If there are a number of particles and their linear momentum is needed, then the linear momentum is defined as the product of the mass of the system and the velocity of the center of mass of the system.

.It can be shown that, in the center of mass frame the momentum of a system is zero.^ In previous examples of collisions and explosions, when we say that the momentum of a system is conserved, it implies that the velocity of the center of mass of the system does not change.

^ If the system was initially at rest, the linear momentum will continue to be zero.

^ Momentum and system of particles If there are a number of particles and their linear momentum is needed, then the linear momentum is defined as the product of the mass of the system and the velocity of the center of mass of the system.

Additionally, the momentum in a frame of reference that is moving at a velocity vcm with respect to that frame is simply: $\mathbf{P}= M\mathbf{v}_ ext{cm}\,\!$
where: $M=\sum_{i = 1}^n m_i\,\!$.
This is known as Euler's first law.

### Relating to force - General equations of motion  Motion of a material body
.The linear momentum of a system of particles can also be defined as the product of the total mass $M\,\!$^ The momentum for such particles is defined as: .

^ Momentum and system of particles If there are a number of particles and their linear momentum is needed, then the linear momentum is defined as the product of the mass of the system and the velocity of the center of mass of the system.

^ The momentum of a system is the same of the momentum of it's particles.

src="http://images-mediawiki-sites.thefullwiki.org/09/1/1/0/6427765214141637.png" /> of the system times the velocity of the center of mass $\mathbf{v}_{cm}\,\!$ $\sum{\mathbf{F}} = {\mathrm{d}\mathbf{P} \over \mathrm{d}t}= M \frac{\mathrm{d}\mathbf{v}_{cm}}{\mathrm{d}t}=M\mathbf{a}_{cm}\,\!$
.This is commonly known as Newton's second law.^ This means that Newton ’s Second Law can be rewritten: .

^ To understand how this comes about, consider first Newton ’s Second Law relating the acceleration a of a body of mass m with an external force F acting on it: .

^ Newton originally stated second law in terms of momentum: .
• Science 122 Program 18 Momentum & Conservation 9 January 2010 19:38 UTC honolulu.hawaii.edu [Source type: FILTERED WITH BAYES]

For a more general derivation using tensors, we consider a moving body (see Figure), assumed as a continuum, occupying a volume $V\,\!$ at a time $t\,\!$, having a surface area $S\,\!$, with defined traction or surface forces $T_i^{(n)}\,\!$ acting on every point of the body surface, body forces $F_i\,\!$ per unit of volume on every point within the volume $V\,\!$, and a velocity field $v_i\,\!$ prescribed throughout the body. Following the previous equation, The linear momentum of the system is: $\int_S T_i^{(n)}dS + \int_V F_i dV = \frac{d}{dt}\int_V \rho \, v_i \, dV\,\!$
By definition the stress vector is $T_i^{(n)} \equiv \sigma_{ij}n_j\,\!$, then $\int_S \sigma_{ij}n_j \, dS + \int_V F_i \, dV = \frac{d}{dt}\int_V \rho \, v_i \, dV\,\!$
Using the Gauss's divergence theorem to convert a surface integral to a volume integral gives (we denote $\partial_j \equiv \frac{\partial}{\partial x_j} \,\!$ as the differential operator): $\int_V \partial_j\sigma_{ij} \, dV + \int_V F_i \, dV = \frac{d}{dt}\int_V \rho \,v_i \, dV\,\!$
.Now we only need to take care of the right side of the equation.^ Jeff K. "I just want to say a quick thank you to Alexander Green for not only his sage advise, but his reassuring words of encouragement that we all need right now."

We have to be careful, since we cannot just take the differential operator under the integral. .This is because while the motion of the continuum body is taking place (the body is not necessarily solid), the volume we are integrating on can change with time too.^ This indicator analyzes actual total changes in a commodities closing price over a predefined amount of time while comparing its traded volumes.

^ Fear” because the last time a large body of squishies jumped on that bandwagon we got to see Newt & Co.
• The Greenroom » Forum Archive » The Momentum of History 9 January 2010 19:38 UTC hotair.com [Source type: Original source]

^ Sometimes the phasing takes place at such a slow rate that it is barely perceivable; at other times it is abrupt and the changes are immediately apparent.
• Petri Kuljuntausta | Momentum 9 January 2010 19:38 UTC www.nic.fi [Source type: General]

So the above integral will be: $\frac{d}{dt}\int \rho \,v_i \, dV=\int \frac{\partial (\rho v_i)}{\partial t}\, dV +\oint \rho v_i v_k n_k dA \,\!$
Performing the differentiation in the first part, and applying the divergence theorem on the second part we obtain: $\frac{d}{dt}\int \rho \,v_i \, dV =\int \left[ \left(\rho\frac{\partial v_i}{\partial t}+v_i\frac{\partial \rho}{\partial t}\right)+\partial_k (\rho v_i v_k)\right]\, dV \,\!$
Now the second term inside the integral is: $\partial_k (\rho v_i v_k)=\rho v_k \cdot \partial_k v_i +v_i\partial_k(\rho v_k) \,\!$. Plugging this into the previous equation, and rearranging the terms, we get: $\frac{d}{dt}\int \rho \,v_i \, dV=\int\rho\left[\frac{\partial}{\partial t}+v_k\partial_k\right]v_i \,dV +\int\left[\frac{\partial\rho}{\partial t}+\partial_k(\rho v_k)\right]v_i \,dV\,\!$
We can easily recognize the two integral terms in the above equation. .The first integral contains the Convective derivative of the velocity vector, and the second integral contains the change and flow of mass in time.^ For the first time in over a century, the Rogue River may flow free of dams for 153 miles to the ocean.

^ IP, G., Market Mass Times Velocity= Momentum.

.Now lets assume that there are no sinks and sources in the system, that is mass is conserved, so this term is zero.^ There can be no better sign that we believe 100% in this revolutionary system.
• OTC Momentum - Catch Momentum in OTC BB and Pink Sheet Stocks 9 January 2010 19:38 UTC www.otcmomentum.com [Source type: FILTERED WITH BAYES]

Hence we obtain: $\frac{d}{dt}\int \rho \,v_i \, dV=\int \rho \,\frac{Dv_i}{Dt} \, dV\,\!$
putting this back into the original equation: $\int_V \left[ \partial_j\sigma_{ij} + F_i - \rho \frac{D v_i}{Dt}\right]\, dV = 0\,\!$
For an arbitrary volume the integrand itself must be zero, and we have the Cauchy's equation of motion $\partial_j\sigma_{ij} + F_i = \rho \frac{D v_i}{Dt}\,\!$
.As we see the only extra assumption we made is that the system doesn't contain any mass sources or sinks, which means that mass is conserved.^ The extra money I made initially using Marks system was in my spare time from my apartment.
• OTC Momentum - Catch Momentum in OTC BB and Pink Sheet Stocks 9 January 2010 19:38 UTC www.otcmomentum.com [Source type: FILTERED WITH BAYES]

So this equation is valid for the motion of any continuum, even for that of fluids. If we are examining elastic continuums only then the second term of the convective derivative operator can be neglected, and we are left with the usual time derivative, of the velocity field.
.If a system is in equilibrium, the change in momentum with respect to time is equal to 0, as there is no acceleration.^ There is no question that the momentum of history has swung to the left, ever since the days of Wilson and Roosevelt.
• The Greenroom » Forum Archive » The Momentum of History 9 January 2010 19:38 UTC hotair.com [Source type: Original source]

^ And he enjoys getting feedback from delighted OTC Momentum™ members saying how the system changed their lives.
• OTC Momentum - Catch Momentum in OTC BB and Pink Sheet Stocks 9 January 2010 19:38 UTC www.otcmomentum.com [Source type: FILTERED WITH BAYES]

^ There can be no better sign that we believe 100% in this revolutionary system.
• OTC Momentum - Catch Momentum in OTC BB and Pink Sheet Stocks 9 January 2010 19:38 UTC www.otcmomentum.com [Source type: FILTERED WITH BAYES] $\sum{\mathbf{F}} = {\mathrm{d}\mathbf{P} \over \mathrm{d}t}=\ M\mathbf{a}_{cm}= 0\,\!$
or using tensors, $\partial_j\sigma_{ij} + F_i = 0\,\!$
These are the equilibrium equations which are used in solid mechanics for solving problems of linear elasticity. In engineering notation, the equilibrium equations are expressed in Cartesian coordinates as $\frac{\partial \sigma_x}{\partial x} + \frac{\partial au_{yx}}{\partial y} + \frac{\partial au_{zx}}{\partial z} + F_x = 0\,\!$ $\frac{\partial au_{xy}}{\partial x} + \frac{\partial \sigma_y}{\partial y} + \frac{\partial au_{zy}}{\partial z} + F_y = 0\,\!$ $\frac{\partial au_{xz}}{\partial x} + \frac{\partial au_{yz}}{\partial y} + \frac{\partial \sigma_z}{\partial z} + F_z = 0\,\!$

## Conservation of linear momentum

The law of conservation of linear momentum is a fundamental law of nature, and it states that the total momentum of a closed system of objects (which has no interactions with external agents) is constant. One of the consequences of this is that the center of mass of any system of objects will always continue with the same velocity unless acted on by a force from outside the system.
.Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum).^ Spectators perceptions of positive momentum while attending NCAA mens and womens basketball regular season contests: Exploring the antecedents-consequences model.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

So, momentum conservation can be philosophically stated as "nothing depends on location per se".
In analytical mechanics the conservation of momentum is a consequence of translational invariance of Lagrangian in the absence of external forces. It can be proven that the total momentum is a constant of motion by making an infinitesimal translation of Lagrangian and then equating it with non translated Lagrangian. This is a special case of Noether's theorem .
.In an isolated system (one where external forces are absent) the total momentum will be constant: this is implied by Newton's first law of motion.^ Momentum Webcast: Consolidating Exchange Server and SQL Server Data Using the HP All-in-One Storage System (Level 200) .
• Momentum: Drive Your Midsize Business Forward 9 January 2010 19:38 UTC www.microsoft.com [Source type: General]

Newton's third law of motion, the law of reciprocal actions, which dictates that the forces acting between systems are equal in magnitude, but opposite in sign, is due to the conservation of momentum.
Since position in space is a vector quantity, momentum (being the canonical conjugate of position) is a vector quantity as well—it has direction. Thus, when a gun is fired, the final total momentum of the system (the gun and the bullet) is the vector sum of the momenta of these two objects. Assuming that the gun and bullet were at rest prior to firing (meaning the initial momentum of the system was zero), the final total momentum must also equal 0.
.In an isolated system with only two objects, the change in momentum of one object must be equal and opposite to the change in momentum of the other object.^ This point is particularly salient for psychological momentum when one considers research into other related subjective experiences such as flow.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

^ Momentum Webcast: Consolidating Exchange Server and SQL Server Data Using the HP All-in-One Storage System (Level 200) .
• Momentum: Drive Your Midsize Business Forward 9 January 2010 19:38 UTC www.microsoft.com [Source type: General]

Mathematically, $\Delta \mathbf{p}_1 = -\Delta \mathbf{p}_2\,\!$
Momentum has the special property that, in a closed system, it is always conserved, even in collisions and separations caused by explosive forces. Kinetic energy, on the other hand, is not conserved in collisions if they are inelastic. .Since momentum is conserved it can be used to calculate an unknown velocity following a collision or a separation if all the other masses and velocities are known.^ Such methods might be used to enable perceptions of momentum to be evaluated in events other than running.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

^ A questionnaire was used to measure perceptions of momentum following a bogus cycle race; the results of which were pre-determined and unaffected by the participants actual performance.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

^ IP, G., Market Mass Times Velocity= Momentum.

A common problem in physics that requires the use of this fact is the collision of two particles. Since momentum is always conserved, the sum of the momenta before the collision must equal the sum of the momenta after the collision: $m_1 \mathbf u_{1} + m_2 \mathbf u_{2} = m_1 \mathbf v_{1} + m_2 \mathbf v_{2} \,\!$
where u1 and u2 are the velocities before collision, and v1 and v2 are the velocities after collision.
Determining the final velocities from the initial velocities (and vice versa) depend on the type of collision. There are two types of collisions that conserve momentum: elastic collisions, which also conserve kinetic energy, and inelastic collisions, which do not.

#### Elastic collisions

A collision between two pool balls is a good example of an almost totally elastic collision, due to their high rigidity; a totally elastic collision exists only in theory, occurring between bodies with mathematically infinite rigidity. In addition to momentum being conserved when the two balls collide, the sum of kinetic energy before a collision must equal the sum of kinetic energy after: $frac{1}{2} m_1 u_{1}^2 + frac{1}{2} m_2 u_{2}^2 = frac{1}{2} m_1 v_{1}^2 + frac{1}{2} m_2 v_{2}^2 \!$
##### In one dimension
When the initial velocities are known, the final velocities for a head-on collision are given by $\mathbf{v}_{1} = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) \mathbf{u}_{1} + \left( \frac{2 m_2}{m_1 + m_2} \right) \mathbf{u}_{2} \!$ $\mathbf{v}_{2} = \left( \frac{m_2 - m_1}{m_1 + m_2} \right) \mathbf{u}_{2} + \left( \frac{2 m_1}{m_1 + m_2} \right) \mathbf{u}_{1}. \!$
When the first body is much more massive than the other (that is, m1m2), the final velocities are approximately given by $\mathbf{v}_{1} = \mathbf{u}_{1} \!$ $\mathbf{v}_{2} = 2\mathbf{u}_{1} - \mathbf{u}_{2}. \!$
Thus the more massive body does not change its velocity, and the less massive body travels at twice the velocity of the more massive body less its own original velocity. .Assuming both masses were heading towards each other on impact, the less massive body is now therefore moving in the opposite direction at twice the speed of the more massive body plus its own original speed.^ Naturally they've been inside the original composition, but now they've got their own acoustical life.
• Petri Kuljuntausta | Momentum 9 January 2010 19:38 UTC www.nic.fi [Source type: General]

^ Other titles In the Beginning and When I am laid in earth might be further hints in that direction; the latter suggests a burial mass.
• Petri Kuljuntausta | Momentum 9 January 2010 19:38 UTC www.nic.fi [Source type: General]  A Newton's cradle demonstrates conservation of momentum.
In a collision between two bodies of equal mass (that is, m1 = m2), the final velocities are given by $\mathbf{v}_1 = \mathbf{u}_2\!$ $\mathbf{v}_2 = \mathbf{u}_1.\!$
Thus the bodies simply exchange velocities. If the first body has nonzero initial velocity u1 and the second body is at rest, then after collision the first body will be at rest and the second body will travel with velocity u1. This phenomenon is demonstrated by Newton's cradle.
##### In multiple dimensions
.In the case of objects colliding in more than one dimension, as in oblique collisions, the velocity is resolved into orthogonal components with one component perpendicular to the plane of collision and the other component or components in the plane of collision.^ Lately, however, it had become more than that -- it had become his damned slogan, inspiration, motivation, and explanation all rolled into one convenient sentence.
• Momentum, a Yu-Gi-Oh fanfic - FanFiction.Net 9 January 2010 19:38 UTC www.fanfiction.net [Source type: Original source]

^ One of us waiting for the tow truck is more than adequate.” “But Niisama,” the younger boy protested, his voice carrying loudly through the lines.
• Momentum, a Yu-Gi-Oh fanfic - FanFiction.Net 9 January 2010 19:38 UTC www.fanfiction.net [Source type: Original source]

^ This point is particularly salient for psychological momentum when one considers research into other related subjective experiences such as flow.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

The velocity components in the plane of collision remain unchanged, while the velocity perpendicular to the plane of collision is calculated in the same way as the one-dimensional case.
For example, in a two-dimensional collision, the momenta can be resolved into x and y components. We can then calculate each component separately, and combine them to produce a vector result. The magnitude of this vector is the final momentum of the isolated system.

#### Perfectly inelastic collisions

A common example of a perfectly inelastic collision is when two snowballs collide and then stick together afterwards. This equation describes the conservation of momentum: $m_1 \mathbf u_{1} + m_2 \mathbf u_{2} = \left( m_1 + m_2 \right) \mathbf v \,\!$
.It can be shown that a perfectly inelastic collision is one in which the maximum amount of kinetic energy is converted into other forms.^ This point is particularly salient for psychological momentum when one considers research into other related subjective experiences such as flow.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

.For instance, if both objects stick together after the collision and move with a final common velocity, one can always find a reference frame in which the objects are brought to rest by the collision and 100% of the kinetic energy is converted.^ We hope this note finds you all happy and healthy and gathering together with loved ones at this time of year.

This is true even in the relativistic case and utilized in particle accelerators to efficiently convert kinetic energy into new forms of mass-energy (i.e. to create massive particles).

#### Coefficient of Restitution

The coefficient of restitution is defined as the ratio of relative velocity of separation to relative velocity of approach. It is a ratio hence it is a dimensionless quantity. The coefficient of restitution is given by: $C_R = \frac{V_{2f} - V_{1f}}{V_{1} - V_{2}}$
for two colliding objects, where
V1f is the scalar final velocity of the first object after impact
V2f is the scalar final velocity of the second object after impact
V1 is the scalar initial velocity of the first object before impact
V2 is the scalar initial velocity of the second object before impact
A perfectly elastic collision implies that CR is 1. So the relative velocity of approach is same as the relative velocity of separation of the colliding bodies.
Inelastic collisions have (CR < 1). In case of a perfectly inelastic collision the relative velocity of separation of the centre of masses of the colliding bodies is 0. Hence the bodies stick together after collision.

#### Explosions

An explosion occurs when an object is divided into two or more fragments due to a release of energy. Note that kinetic energy in a system of explosion is not conserved because it involves energy transformation (i.e. kinetic energy changes into heat and acoustic energy).
See the inelastic collision page for more details.

## Modern definitions of momentum

### Momentum in relativistic mechanics

In relativistic mechanics, in order to be conserved, the momentum of an object must be defined as $\mathbf{p} = \gamma m_0\mathbf{v} \,\!$
where m0 is the invariant mass of the object and γ is the Lorentz factor, given by $\gamma = \frac{1}{\sqrt{1 - (v/c)^2}},\,\!$
where v is the speed of the object and c is the speed of light.
Relativistic momentum can also be written as invariant mass times the object's proper velocity, defined as the rate of change of object position in the observer frame with respect to time elapsed on object clocks (i.e. object proper time). Within the domain of classical mechanics, relativistic momentum closely approximates Newtonian momentum: at low velocity, γm0v is approximately equal to m0v, the Newtonian expression for momentum.  A graphical representation of the interrelation of relativistic energy E, invariant mass m0, relativistic momentum p, and relativistic mass m = γm0.
The total energy E of a body is related to the relativistic momentum p by $E^2 = (pc)^2 + (m_0c^2)^2,\,\!$
where p denotes the magnitude of p. This relativistic energy-momentum relationship holds even for massless particles such as photons; by setting m0 = 0 it follows that $E = pc.\,\!$
For both massive and massless objects, relativistic momentum is related to the de Broglie wavelength λ by $p = h/\lambda,\,\!$
where h is the Planck constant.

#### Four-vector formulation

Relativistic four-momentum as proposed by Albert Einstein arises from the invariance of four-vectors under Lorentzian translation. The four-momentum P is defined as: $\mathbf{P} := (E/c, p_x , p_y ,p_z)\,\!$
where E = γm0c2 is the total relativistic energy of the system, and px, py, and pz represent the x-, y-, and z-components of the relativistic momentum, respectively.
The magnitude ||P|| of the momentum four-vector is equal to m0c, since $||\mathbf{P}||^2 = (E/c)^2 - p^2 = (m_0c)^2.\,\!$
which is invariant across all reference frames.

#### Generalization of momentum

Momentum is the Noether charge of translational invariance. .As such, even fields as well as other things can have momentum, not just particles.^ Such methods might be used to enable perceptions of momentum to be evaluated in events other than running.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

^ This point is particularly salient for psychological momentum when one considers research into other related subjective experiences such as flow.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

^ Those kind of things gave a guy something about which to think, even someone like Jounouchi who deplored such introspection and analysis.
• Momentum, a Yu-Gi-Oh fanfic - FanFiction.Net 9 January 2010 19:38 UTC www.fanfiction.net [Source type: Original source]

However, in curved space-time which is not asymptotically Minkowski, momentum isn't defined at all.

### Momentum in quantum mechanics

In quantum mechanics, momentum is defined as an operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are conjugate variables.
For a single particle described in the position basis the momentum operator can be written as $\mathbf{p}={\hbar\over i} abla=-i\hbar abla\,\!$
where ∇ is the gradient operator, ħ is the reduced Planck constant, and i is the imaginary unit. This is a commonly encountered form of the momentum operator, though the momentum operator in other bases can take other forms, for example in the momentum basis the momentum operator is represented as $\mathbf{p}\psi(p) = p\psi(p),\!$
where the operator p acting on a wave function ψ(p) yields that wave function multiplied by the value p, in an analogous fashion to the way that the position operator acting on a wave function ψ(x) yields that wave function multiplied by the value x.

### Momentum in electromagnetism

Electric and magnetic fields possess momentum regardless of whether they are static or they change in time. The pressure, P, of an electrostatic (magnetostatic) field upon a metal sphere, cylindrical capacitor or ferromagnetic bar is: $P_{static} = {W}= \left[ {\epsilon_0 \epsilon}{\frac{{\mathbf E}^2 }{ {2}}} +{\frac{ 1 }{ {\mu_0 \mu} }} {\frac{{\mathbf B}^2}{{2}}} \right],\,\!$
where ${W}\,\!$, ${\mathbf E}\,\!$, ${\mathbf B}\,\!$, are the electromagnetic energy density, electric field, and magnetic field respectively. The electromagnetic pressure ${P}={W}\,\!$ may be sufficiently high to explode the capacitor. Thus electric and magnetic fields do carry momentum.
Light (visible, UV, radio) is an electromagnetic wave and also has momentum. .Even though photons (the particle aspect of light) have no mass, they still carry momentum.^ In fact, even after a half-day’s work on them, they still were present in his mind.
• Momentum, a Yu-Gi-Oh fanfic - FanFiction.Net 9 January 2010 19:38 UTC www.fanfiction.net [Source type: Original source]

^ Now that NBA season is upon us im excited…even though there is no team in my immediate area…” .
• SonicsCentral.com - Massive Monkeys Representing » Blog Archive » Momentum … 9 January 2010 19:38 UTC sonicscentral.com [Source type: General]

^ Now that NBA season is upon us im excited…even though there is no team in my immediate area… .
• SonicsCentral.com - Massive Monkeys Representing » Blog Archive » Momentum … 9 January 2010 19:38 UTC sonicscentral.com [Source type: General]

This leads to applications such as the solar sail. The calculation of the momentum of light is controversial (see Abraham–Minkowski controversy ).
.Momentum is conserved in an electrodynamic system (it may change from momentum in the fields to mechanical momentum of moving parts).^ These researchers conceptualized psychological momentum as a perception of moving towards a goal, which yielded changes in motivation, perceptions of control, optimism, energy and synchronization.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

.The treatment of the momentum of a field is usually accomplished by considering the so-called energy-momentum tensor and the change in time of the Poynting vector integrated over some volume.^ Indeed, it is usual for conceptual models to be developed following the establishment of clear conceptualizations of the phenomena, which is not the case when one considers psychological momentum.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

^ First, he’d call the automotive repair shop where his cars were usually serviced, then he’d call Mokuba to tell him of the change in plans.
• Momentum, a Yu-Gi-Oh fanfic - FanFiction.Net 9 January 2010 19:38 UTC www.fanfiction.net [Source type: Original source]

^ These researchers conceptualized psychological momentum as a perception of moving towards a goal, which yielded changes in motivation, perceptions of control, optimism, energy and synchronization.
• Athletic Insight - A Review of Psychological Momentum in Sports: Why qualitative research is needed. 9 January 2010 19:38 UTC www.athleticinsight.com [Source type: Academic]

This is a tensor field which has components related to the energy density and the momentum density.
The definition canonical momentum corresponding to the momentum operator of quantum mechanics when it interacts with the electromagnetic field is, using the principle of least coupling: $\mathbf P = m\mathbf v + q\mathbf A\,\!$,
instead of the customary $\mathbf p = m\mathbf v\,\!$,
where: $\mathbf A\,\!$ is the electromagnetic vector potential $m\,\!$ the charged particle's invariant mass $\mathbf v\,\!$ its velocity $q\,\!$ its charge.

## Notes

1. ^ Lewis, Charleton T.; Charles Short. "mōtus" (html). A Latin Dictionary. Tufts University: The Perseus Project. Retrieved 2008-02-15.
2. ^ A. Sayili (1987). "Ibn Sīnā and Buridan on the Motion of the Projectile". Annals of the New York Academy of Sciences 500 (1): 477–482. "Thus he considered impetus as proportional to weight times velocity. Avicenna was later to be given the title of the father of momentum. In other words, his conception of impetus comes very close to the concept of momentum of Newtonian mechanics.".
3. ^ Daniel Garber (1992). "Descartes' Physics". in John Cottingham. The Cambridge Companion to Descartes. Cambridge: Cambridge University Press. p. 310-319. ISBN 0-521-36696-8.
4. ^ Scott, J.F. (1981). The Mathematical Work of John Wallis, D.D., F.R.S.. Chelsea Publishing Company. pp. 111. ISBN 0828403147.
5. ^ Newton placed his definitions up front as did Wallis, with whom Newton can hardly fail to have been familiar.
6. ^ Grimsehl, Ernst; Leonard Ary Woodward, Translator (1932). A Textbook of Physics. London, Glasgow: Blackie & Son limited. pp. 78.
7. ^ Rescigno, Aldo (2003). Foundation of Pharmacokinetics. New York: Kluwer Academic/Plenum Publishers. pp. 19.
8. ^ Jennings, John (1721). Miscellanea in Usum Juventutis Academicae. Northampton: R. Aikes & G. Dicey. pp. 67.
9. ^ "Euler's Laws of Motion". Retrieved 2009-03-30.
10. ^ McGill and King (1995). Engineering Mechanics, An Introduction to Dynamics (3rd ed.). PWS Publishing Company. ISBN 0-534-93399-8.
11. ^ Hand, Louis N.; Finch, Janet D.. Analytical Mechanics. Cambridge University Press. Chapter 4.

## References

• Halliday, David; Robert Resnick (1960-2007). Fundamentals of Physics. John Wiley & Sons. Chapter 9.
• Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6 ed.). Brooks Cole. ISBN 0-534-40842-7
• Stenger, Victor J. (2000). Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Prometheus Books. Chpt. 12 in particular.
• Tipler, Paul (1998). Physics for Scientists and Engineers: Vol. 1: Mechanics, Oscillations and Waves, Thermodynamics (4th ed.). W. H. Freeman. ISBN 1-57259-492-6
• Hand, Louis N.; Finch, Janet D.. Analytical Mechanics. Cambridge University Press. Chapter 4.

# Wikispecies

Up to date as of January 23, 2010

### From Wikispecies

Main Page
Supergroup: Unikonta
Regnum: Animalia
Subregnum: Eumetazoa
Phylum: Arthropoda
Subphylum: Hexapoda
Classis: Insecta
Superordo: Coleopterida
Ordo: Coleoptera
Subordo: Polyphaga
Infraordo: Elateriformia
Superfamilia: Byrrhoidea
Familia: Dryopidae
Genus: Momentum
Species: M. detectum - M. hirsutum - M. hispidum - M. longipalpis - M. minimum - M. pusillum - M. reburrum - M. sensorium

## Name

Momentum Perkins, 1997

## References

• Hinton, H.E. 1937: Protoparnus pusillus, new species of Dryopidae from St. Vincent (Coleoptera). Revue d'Entomologie, 7: 302-306.
• Ivie, M.A. 1985: Note on habitat and distribution of Protoparnus pusillus Hinton in the Lesser Antilles (Coleoptera: Dryopidae). Coleopterists bulletin, 39: 35.
• Perkins, P.D. 1997: Momentum and Ghiselinius, new Neotropical genera of humicolous beetles with remarkable and divergent mouthparts (Coleoptera: Dryopidae). Studies on Neotropical fauna and environment, 32(2): 100-117.

# Simple English

Simply speaking, momentum of an object (p) is defined as the product of the mass (m) and velocity (v) of the object. It is a vector quantity, which has both direction and magnitude. Its unit is kg/ms (kilo-gramme per meter-second) or Ns (Newton second). Momentum is sometimes referred to as linear momentum which is different from its related subject angular momentum.

Momentum is a conserved object, meaning that the total initial momentum of a system must be equal to the total final momentum of a system. Total amount of momentum remains unchanged.

Momentum can be considered the "power" when an object is moving, meaning how much force it can have on another object. For example, a bowling ball (large mass) pushed very slowly (low velocity) can hit a glass door and not break it, while a baseball (small mass) can be thrown fast (high velocity) and break the same window. The baseball has a larger momentum than the bowling ball. Because momentum is the product of the mass and the velocity of an object, that both mass and velocity affect the momentum of an object. As shown, an object with a large mass and low velocity can have the same momentum as an object with a small mass and large velocity.

## Formula

In Newtonian physics, the usual symbol for momentum is a p ; so this can be written

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

where p is the momentum, m is the mass and v is the velocity.
If we apply Newton's 2nd Law, we can derive

$\mathbf\left\{F\right\}= \left\{mv-mu\over\ t\right\} \,,$

The meaning is that the net force on an object is equal to the rate of change in momentum of the object.

This equation also applies in special relativity, but with m being the relativistic mass of the object.

## Impulse

Impulse is the change in momentum cause by a net force:

## Law of conservation of momentum

In understanding conservation of momentum, the direction of the momentum is important. Momentum in a system is added up using vector addition. Under the rules of vector addition, adding a certain amount of momentum together with the same amount of momentum going in the opposite direction gives a total momentum of zero.

For instance, when a gun is fired, a small mass (the bullet) moves at a high speed in one direction. A larger mass (the gun) moves in the opposite direction at a much slower speed. The momentum of the bullet and the momentum of the gun are exactly equal in size but opposite in direction. Using vector addition to add the momentum of the bullet to the momentum of the gun (equal in size but opposite in direction) gives a total system momentum of zero. The momentum of the gun-bullet system has been conserved.

# Citable sentences

Up to date as of December 29, 2010

Here are sentences from other pages on Momentum, which are similar to those in the above article.