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'''Импулсот''' <math>\vec{p}</math> (постаро име: '''количество движење'''), '''момент''' или '''залет''' — во [[механика]]та претставува [[физичка величина]] што ја карактеризира мерката на механичкото [[Движење (физика)|движење]] на телата. Во [[Класична механика|класичната механика]], импулсот на телата е еднаков на производот од [[маса]]та <math>m\,</math> на телото (материјалната точка) и неговата [[брзина]] <math>\vec{v}</math>; насоката на импулсот се совпаѓа со насоката на [[вектор]]от на брзината:
{{Во изработка}}
: <math>\vec p=m\vec v</math>.
{{Infobox physical quantity
Единица мерка за импулсот во [[SI]] е [[Килограм|кг]]·[[Метар во секунда|м/с]] (kg·m/s).
| name = Momentum
| image = [[File:Billard.JPG|frameless|A pool break-off shot]]
| caption = Momentum of a [[Pool (cue sports)|pool]] cue ball is transferred to the racked balls after collision.
| unit = [[kilogram metre per second|kilogram meter per second]] kg · m/s
|otherunits = [[slug (mass)|slug]] · [[foot per second|ft/s]]
| symbols = ''p'', '''p'''
|conserved = yes
}}
'''Линиски импулс, транслаторен импулс''' или едноставно само '''импулс''' е производ на [[Маса|масата]] и [[Брзина|брзината]] на едно тело и се мери во единица килограм на метар по секунда. [[Димензија|Димензионално]] е еднаква со импулсот или производот од [[Сила|силата]] и [[Време|времето]], и се мери како њутни во секунда. [[Newton's second law]] of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. For example, a heavy truck moving rapidly has a large momentum, and it takes a large or prolonged force to get the truck up to this speed, and would take a similarly large or prolonged force to bring it to a stop. If the truck were lighter, or moving more slowly, then it would have less moment
{{Classical mechanics |fundamentals |width=20.55em}}
um and therefore require less impulse to start or stop.
Во најопшт случај, импулсот на некое тело концептуално може да се сфати како настојување на тоа тело да го продолжи движењето во ист правец и насока, доколку на него не дејствува некоја надворешна сила. Во согласност со ова тој е природна последица на [[Њутнови закони|Њутновите закони]] за движењето.
Like velocity, linear momentum is a [[Euclidean vector|vector]] quantity, possessing a direction as well as a magnitude:
:<math>\mathbf{p} = m \mathbf{v},</math>
Импулсот е конзервирана (зачувана) величина, што значи дека вкупниот импулс на било кој [[изолиран систем]] (систем кој не е под влијание на надворешни сили) не може да се промени.
where {{math|'''p'''}} is the three-dimensional vector stating the object's momentum in the three directions of three-dimensional space, {{math|'''v'''}} is the three-dimensional velocity vector giving the object's rate of movement in each direction, and {{math|''m''}} is the object's mass.
Концептот за импулсот е воведен во класичната механика благодарение на голем број познати мислители и експериментатори, како што се [[Рене Декарт]], [[Галилео Галилеј]], [[Исак Њутн]], [[Готфрид Лајбниц]] и други.
Linear momentum is also a ''conserved'' quantity, meaning that if a [[closed system]] is not affected by external forces, its total linear momentum cannot change.
== Импулс на систем од тела ==
In classical mechanics, [[#Conservation|conservation of linear momentum]] is implied by [[Newton's laws]].<ref>{{cite book |title=Invitation to Contemporary Physics |edition=illustrated |first1=Quang |last1=Ho-Kim |first2=Narendra |last2=Kumar |first3=Harry C. S. |last3= Lam |publisher=World Scientific |year=2004 |isbn=978-981-238-303-7 |page=19 |url=https://books.google.com/books?id=Lxr2S-zjOgYC}} [https://books.google.com/books?id=Lxr2S-zjOgYC&pg=PA19 Extract of page 19]</ref> It also holds in [[special relativity]] (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum [[Conservation law (physics)|conservation law]] holds in [[electrodynamics]], [[quantum mechanics]], [[quantum field theory]], and [[general relativity]]. It is ultimately an expression of one of the fundamental symmetries of space and time, that of [[translational symmetry]].
[[Податотека:Billard.JPG|мини|десно|250п|Импулсот на белата топка се пренесува на сите останати топки.]]
=== Во зависност од масата и брзината на телото ===
Во класичната механика, вкупниот импулс на даден систем од тела (или честици) е векторски збир од импулсите на сите поединечни тела во системот:
Linear momentum depends on frame of reference. Observers in different frames would find different values of linear momentum of a system. But each would observe that the value of linear momentum does not change with time, provided the system is isolated.
:<math>\vec p= \sum_{i = 1}^n m_i \vec\mathbf{v}_i = m_1 \vec\mathbf{v}_1 + m_2 \vec\mathbf{v}_2 + m_3 \vec\mathbf{v}_3 + ... + m_n \vec\mathbf{v}_n </math>
каде:
:<math>\vec p</math> е импулсот на системот
:<math> m_i\, </math> е масата на телото i
:<math>\vec\mathbf{v}_i</math> е брзината на телото i
:<math> n\ </math> е бројот на телата во системот.
=== Во врска со силата ===
{{TOC limit|3}}
Според [[Втор Њутнов закон|Вториот Њутнов закон]], [[сила]]та е еднаква на промената на импулсот во единица време (прв [[извод]] на импулсот по времето):
==Newtonian mechanics==
: <math>\vec{F} = {\mathrm{d}\vec{p} \over \mathrm{d}t}</math>.
Momentum has a direction as well as magnitude. Quantities that have both a magnitude and a direction are known as [[Euclidean vector|vector]] quantities. Because momentum has a direction, it can be used to predict the resulting direction of objects after they collide, as well as their speeds. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations (see [[Momentum#Multiple dimensions|multiple dimensions]]).
Кога масата на телото е постојана се применува вообичаената равенка за сила (основна равенка на [[Динамика (физика)|динамиката]]), односно <math>\vec{F} = m\vec{a} </math>. Олеснувачка околност е што овој случај е многу чест.
===Single particle===
The momentum of a particle is traditionally represented by the letter {{math|''p''}}. It is the product of two quantities, the [[mass]] (represented by the letter {{math|''m''}}) and [[velocity]] ({{math|''v''}}):<ref name=FeynmanCh9>{{harvnb|Feynman Vol. 1|loc=Chapter 9}}</ref>
:<math>p = m v. </math>
The units of momentum are the product of the units of mass and velocity. In [[SI units]], if the mass is in kilograms and the velocity in meters per second then the momentum is in kilogram meters/second (kg m/s). In [[Centimetre–gram–second system of units|cgs units]], if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters/second (g cm/s).
Being a vector, momentum has magnitude and direction. For example, a 1 kg model airplane, 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.
===Many particles===
The momentum of a system of particles is the sum of their momenta. If two particles have masses {{math|''m''<sub>1</sub>}} and {{math|''m''<sub>2</sub>}}, and velocities {{math|''v''<sub>1</sub>}} and {{math|''v''<sub>2</sub>}}, the total momentum is
:<math> \begin{align} p &= p_1 + p_2 \\
&= m_1 v_1 + m_2 v_2\,. \end{align} </math>
The momenta of more than two particles can be added more generally with the following:
:<math> p=\sum_{i}m_iv_i </math>
A system of particles has a [[center of mass]], a point determined by the weighted sum of their positions:
:<math> r_\text{cm} = \frac{m_1 r_1 + m_2 r_2 + \cdots}{m_1 + m_2 + \cdots} = \frac{\sum\limits_{i}m_ir_i}{\sum\limits_{i}m_i}.</math>
If all the particles are moving, the center of mass will generally be moving as well (unless the system is in pure rotation around it). If the center of mass is moving at velocity {{math|''v''<sub>cm</sub>}}, the momentum is:
:<math>p= mv_\text{cm}.</math>
This is known as [[Euler's laws of motion|Euler's first law]].<ref name="BookRags">{{cite web
|url=http://www.bookrags.com/research/eulers-laws-of-motion-wom/
|title=Euler's Laws of Motion
|accessdate=2009-03-30}}</ref><ref name="McGillKing">{{cite book
|title=Engineering Mechanics, An Introduction to Dynamics
|edition=3rd
|last=McGill and King
|publisher=PWS Publishing Company
|date=1995
|isbn=0-534-93399-8}}</ref>
===Relation to force===
If a force {{math|''F''}} is applied to a particle for a time interval {{math|Δ''t''}}, the momentum of the particle changes by an amount
:<math>\Delta p = F \Delta t\,.</math>
In differential form, this is [[Newton's second law]]; the rate of change of the momentum of a particle is proportional to the force {{math|''F''}} acting on it,<ref name=FeynmanCh9/>
:<math>F = \frac{dp }{d t}. </math>
If the force depends on time, the change in momentum (or [[impulse (physics)|impulse]] {{math|''J''}}) between times {{math|''t''<sub>1</sub>}} and {{math|''t''<sub>2</sub>}} is
:<math> \Delta p = J = \int_{t_1}^{t_2} F(t)\, dt\,.</math>
Impulse is measured in the [[SI derived unit|derived unit]]s of the [[newton second]] (1 N s = 1 kg m/s) or [[dyne]] second (1 dyne s = 1 g m/s)
Under the assumption of constant mass {{math|''m''}}, it is equivalent to write
:<math>F = m\frac{dv}{d t} = m a,</math>
so the force is equal to mass times [[acceleration]].<ref name=FeynmanCh9/>
''Example'': A model airplane of 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The net force required to produce this acceleration is 3 [[newton (unit)|newtons]] due north. The change in momentum is 6 kg m/s. The rate of change of momentum is 3 (kg m/s)/s = 3 N.
===Conservation===
[[File:Newtons cradle animation book 2.gif|thumb|[[Њутнова лулашка]] која го прикажува зачувувањето на импулсот.]]
In a [[closed system]] (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum is constant. This fact, known as the ''law of conservation of momentum'', is implied by [[Newton's laws of motion]].<ref name=FeynmanCh10>{{harvnb|Feynman Vol. 1|loc=Chapter 10}}</ref> Suppose, for example, that two particles interact. Because of the third law, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second law states that {{math|''F''<sub>1</sub> {{=}} {{sfrac|''dp''<sub>1</sub>|''dt''}}}} and {{math|''F''<sub>2</sub> {{=}} {{sfrac|''dp''<sub>2</sub>|''dt''}}}}. Therefore,
:<math> \frac{d p_1}{d t} = - \frac{d p_2}{d t}, </math>
with the negative sign indicating that the forces oppose. Equivalently,
:<math> \frac{d}{d t} \left(p_1+ p_2\right)= 0. </math>
If the velocities of the particles are {{math|''u''<sub>1</sub>}} and {{math|''u''<sub>2</sub>}} before the interaction, and afterwards they are {{math|''v''<sub>1</sub>}} and {{math|''v''<sub>2</sub>}}, then
:<math>m_1 u_{1} + m_2 u_{2} = m_1 v_{1} + m_2 v_{2}.</math>
This law holds no matter how complicated the force is between particles. Similarly, if there are several particles, the momentum exchanged between each pair of particles adds up to zero, so the total change in momentum is zero. This conservation law applies to all interactions, including [[collision]]s and separations caused by explosive forces.<ref name=FeynmanCh10/> It can also be generalized to situations where Newton's laws do not hold, for example in the [[theory of relativity]] and in [[Classical electromagnetism|electrodynamics]].<ref name=Goldstein54/>
===Dependence on reference frame===
[[File:Relativity an apple in a lift.svg|thumb|Newton's apple in Einstein's elevator. In person A's frame of reference, the apple has non-zero velocity and momentum. In the elevator's and person B's frames of reference, it has zero velocity and momentum.]]
Momentum is a measurable quantity, and the measurement depends on the motion of the observer. For example: if an apple is sitting in a glass elevator that is descending, an outside observer, looking into the elevator, sees the apple moving, so, to that observer, the apple has a non-zero momentum. To someone inside the elevator, the apple does not move, so, it has zero momentum. The two observers each have a [[frame of reference]], in which, they observe motions, and, if the elevator is descending steadily, they will see behavior that is consistent with those same physical laws.
Suppose a particle has position {{math|''x''}} in a stationary frame of reference. From the point of view of another frame of reference, moving at a uniform speed {{math|''u''}}, the position (represented by a primed coordinate) changes with time as
:<math> x' = x - ut\,.</math>
This is called a [[Galilean transformation]]. If the particle is moving at speed {{math|{{sfrac|''dx''|''dt''}} {{=}} ''v''}} in the first frame of reference, in the second, it is moving at speed
:<math> v' = \frac{dx'}{dt} = v-u\,.</math>
Since {{math|''u''}} does not change, the accelerations are the same:
:<math> a' = \frac{dv'}{dt} = a\,.</math>
Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton's second law is unchanged. Forces such as Newtonian gravity, which depend only on the scalar distance between objects, satisfy this criterion. This independence of reference frame is called Newtonian relativity or [[Galilean invariance]].<ref>{{harvnb|Goldstein|1980|p=276}}</ref>
A change of reference frame, can, often, simplify calculations of motion. For example, in a collision of two particles, a reference frame can be chosen, where, one particle begins at rest. Another, commonly used reference frame, is the [[center of mass frame]] - one that is moving with the center of mass. In this frame,
the total momentum is zero.
Кога системот се наоѓа во рамнотежа, тогаш промената на импулсот во единица време (силата која дејствува на системот) е еднаква на 0, т.е.
<math>\vec{F} = {\mathrm{d}\vec{p} \over \mathrm{d}t}</math> = <math>\ m\vec{a} </math> = 0
[[Категорија:Класична механика]]
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