Force

=== Third law ===
{{main|Newton's third law}}
Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if <math>\vec{F}_{1,2}</math> is the force of body 1 on body 2 and <math>\vec{F}_{2,1}</math> that of body 2 on body 1, then
<math display="block">\vec{F}_{1,2}=-\vec{F}_{2,1}.</math>
This law is sometimes referred to as the ''action-reaction law'', with <math> \vec{F}_{1,2}</math> called the ''action'' and <math> -\vec{F}_{2,1}</math> the ''[[Reaction (physics)|reaction]]''.

Newton's Third Law is a result of applying [[symmetry]] to situations where forces can be attributed to the presence of different objects. The third law means that all forces are ''interactions'' between different bodies.<ref>{{cite journal
|title=Newton's third law revisited
|first=C. |last=Hellingman
|journal=Phys. Educ.
|volume=27
|year=1992
|issue=2
|pages=112–115
|quote=Quoting Newton in the ''Principia'': It is not one action by which the Sun attracts Jupiter, and another by which Jupiter attracts the Sun; but it is one action by which the Sun and Jupiter mutually endeavour to come nearer together.
|doi=10.1088/0031-9120/27/2/011 |bibcode=1992PhyEd..27..112H |s2cid=250891975
}}</ref><ref>{{Cite book |last1=Resnick |first1=Robert |title=Physics. 1 |last2=Halliday |first2=David |last3=Krane |first3=Kenneth S. |date=2002 |isbn=978-0-471-32057-9 |edition=5|quote="Any single force is only one aspect of a mutual interaction between ''two'' bodies."}}</ref> and thus that there is no such thing as a unidirectional force or a force that acts on only one body.

In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero:
<math display="block">\vec{F}_{1,2}+\vec{F}_{2,1}=0.</math>
More generally, in a [[closed system]] of particles, all internal forces are balanced. The particles may accelerate with respect to each other but the [[center of mass]] of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system.<ref name=FeynmanVol1 />{{rp|((19-1))}}<ref name=Kleppner />

Combining Newton's Second and Third Laws, it is possible to show that the [[Conservation of momentum|linear momentum of a system is conserved]] in any [[closed system]]. In a system of two particles, if <math> \vec{p}_1</math> is the momentum of object 1 and <math> \vec{p}_{2}</math> the momentum of object 2, then
<math display="block">\frac{\mathrm{d}\vec{p}_1}{\mathrm{d}t} + \frac{\mathrm{d}\vec{p}_2}{\mathrm{d}t}= \vec{F}_{1,2} + \vec{F}_{2,1} = 0.</math>
Using similar arguments, this can be generalized to a system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained.<ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner />