From Wikipedia, the free encyclopedia
Momentum

Expressed in (SI unit): 
kg · m/s 
Commonly used symbols: 
p 
Conserved: 
yes 
Expressed in other quantities: 
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.
.^ 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.
.^ 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.
.^ 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]
.^ 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]
.^ 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]
.^ 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
.^ 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,
^{[1]} while
velocitas, "swiftness", captured only
speed.
.^ 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.
.^ 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.
^{[2]}
.^ 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.
.^ 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]
.^ 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.
^{[3]} 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.
.^ 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.
.^ 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.
.^ 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]
.^ 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.
.^ 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.
^{[6]} .^ 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.
^{[7]} .^ 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.
.^ 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 .
^{[8]}
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.
.^ 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.
.^ Learn how trend and momentum determines the rite time frame at those all important market turns.
.^ 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.
.^ How to Gauge momentum in each time frame.
^ 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.
.^ 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
where
.^ 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.
.^ 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]
.^ 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]
.^ 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 .
.^ 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 5kg object experiences a 10N force for a duration of 0.10second, 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: .
or just simply
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.
.^ This impulse would cause a momentum change of 720 kgm/s.
^ If a 5kg object experiences a 10N force for a duration of 0.10second, then what is the momentum change of the object?
.^ When force is zero, there is no change in momentum.
^ Title changed to "momentum" from "momentum (nonrelativistic)", 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:
where
.^ 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.
.^ 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
v_{cm} with respect to that frame is simply:
where:
 .
Relating to force  General equations of motion
Motion of a material body
.^ 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
at a time
, having a surface area
, with defined traction or surface forces
acting on every point of the body surface, body forces
per unit of volume on every point within the volume
, and a velocity field
prescribed throughout the body. Following the previous equation, The linear momentum of the system is:
By definition the
stress vector is
, then
Using the
Gauss's divergence theorem to convert a surface integral to a volume integral gives (we denote
as the differential operator):
.^ 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 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:
Performing the differentiation in the first part, and applying the divergence theorem on the second part we obtain:
Now the second term inside the integral is:
. Plugging this into the previous equation, and rearranging the terms, we get:
We can easily recognize the two integral terms in the above equation.
.^ 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.
.^ 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:
putting this back into the original equation:
.^ 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.
.^ 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]
or using tensors,
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.
.^ Spectators perceptions of positive momentum while attending NCAA mens and womens basketball regular season contests: Exploring the antecedentsconsequences 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".
.^ Momentum Webcast: Consolidating Exchange Server and SQL Server Data Using the HP AllinOne 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.
.^ 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 AllinOne Storage System (Level 200) . Momentum: Drive Your Midsize Business Forward 9 January 2010 19:38 UTC www.microsoft.com [Source type: General]
Mathematically,
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.
.^ 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 predetermined 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:
where u_{1} and u_{2} are the velocities before collision, and v_{1} and v_{2} 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:
In one dimension
When the initial velocities are known, the final velocities for a headon collision are given by
When the first body is much more massive than the other (that is, m_{1} ≫ m_{2}), the final velocities are approximately given by
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.
.^ 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]
In a collision between two bodies of equal mass (that is, m_{1} = m_{2}), the final velocities are given by
Thus the bodies simply exchange velocities. If the first body has nonzero initial velocity
u_{1} 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
u_{1}. This phenomenon is demonstrated by
Newton's cradle.
In multiple dimensions
.^ 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 YuGiOh 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 YuGiOh 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 onedimensional case.
For example, in a twodimensional 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:

.^ 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]
.^ 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
massenergy (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:
for two colliding objects, where
 V_{1f} is the scalar final velocity of the first object after impact
 V_{2f} is the scalar final velocity of the second object after impact
 V_{1} is the scalar initial velocity of the first object before impact
 V_{2} is the scalar initial velocity of the second object before impact
A perfectly elastic collision implies that C_{R} is 1. So the relative velocity of approach is same as the relative velocity of separation of the colliding bodies.
Inelastic collisions have (C_{R} < 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).
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
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,
γm_{0}v is approximately equal to
m_{0}v, the Newtonian expression for momentum.
A graphical representation of the interrelation of relativistic energy
E, invariant mass
m_{0}, relativistic momentum
p, and
relativistic mass m = γm_{0}.
The total energy E of a body is related to the relativistic momentum p by
where p denotes the magnitude of p. This relativistic energymomentum relationship holds even for massless particles such as photons; by setting m_{0} = 0 it follows that
For both massive and massless objects, relativistic momentum is related to the
de Broglie wavelength λ by
Fourvector formulation
where E = γm_{0}c^{2} is the total relativistic energy of the system, and p_{x}, p_{y}, and p_{z} represent the x, y, and zcomponents of the relativistic momentum, respectively.
The magnitude P of the momentum fourvector is equal to m_{0}c, since
which is invariant across all reference frames.
Generalization of momentum
Momentum is the
Noether charge of translational invariance.
.^ 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 YuGiOh fanfic  FanFiction.Net 9 January 2010 19:38 UTC www.fanfiction.net [Source type: Original source]
However, in
curved spacetime which is not asymptotically
Minkowski, momentum isn't defined at all.
Momentum in quantum mechanics
For a single particle described in the position basis the momentum operator can be written as
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
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:
where
,
,
, are the electromagnetic energy density, electric field, and magnetic field respectively. The electromagnetic pressure
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.
.^ In fact, even after a halfday’s work on them, they still were present in his mind. Momentum, a YuGiOh 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 [1]).
.^ 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]
.^ 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 YuGiOh 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:
 ,
instead of the customary
 ,
where:
 is the electromagnetic vector potential
 the charged particle's invariant mass
 its velocity
 its charge.
See also
Notes
 ^ Lewis, Charleton T.; Charles Short. "mōtus" (html). A Latin Dictionary. Tufts University: The Perseus Project. http://www.perseus.tufts.edu/cgibin/ptext?doc=Perseus%3Atext%3A1999.04.0059%3Aentry%3D%2329780. Retrieved 20080215.
 ^ 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.".
 ^ Daniel Garber (1992). "Descartes' Physics". in John Cottingham. The Cambridge Companion to Descartes. Cambridge: Cambridge University Press. p. 310319. ISBN 0521366968. http://www.cup.es/us/catalogue/catalogue.asp?isbn=9780521366960.
 ^ Scott, J.F. (1981). The Mathematical Work of John Wallis, D.D., F.R.S.. Chelsea Publishing Company. pp. 111. ISBN 0828403147.
 ^ Newton placed his definitions up front as did Wallis, with whom Newton can hardly fail to have been familiar.
 ^ Grimsehl, Ernst; Leonard Ary Woodward, Translator (1932). A Textbook of Physics. London, Glasgow: Blackie & Son limited. pp. 78.
 ^ Rescigno, Aldo (2003). Foundation of Pharmacokinetics. New York: Kluwer Academic/Plenum Publishers. pp. 19.
 ^ Jennings, John (1721). Miscellanea in Usum Juventutis Academicae. Northampton: R. Aikes & G. Dicey. pp. 67.
 ^ "Euler's Laws of Motion". http://www.bookrags.com/research/eulerslawsofmotionwom/. Retrieved 20090330.
 ^ McGill and King (1995). Engineering Mechanics, An Introduction to Dynamics (3rd ed.). PWS Publishing Company. ISBN 0534933998.
 ^ Hand, Louis N.; Finch, Janet D.. Analytical Mechanics. Cambridge University Press. Chapter 4.
References
 Halliday, David; Robert Resnick (19602007). Fundamentals of Physics. John Wiley & Sons. Chapter 9.
 Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6 ed.). Brooks Cole. ISBN 0534408427
 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 1572594926
 Hand, Louis N.; Finch, Janet D.. Analytical Mechanics. Cambridge University Press. Chapter 4.
External links