Editing Newton's laws of motion (section)

===Third law{{anchor|Newton's_third_law}}===
:''To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.''<ref name=":0" />{{Rp|page=116}}
[[File:Iridium-1 Launch (32312419215).jpg|thumb|upright|[[Rocket]]s work by creating unbalanced high pressure that pushes the rocket upwards while exhaust gas exits through an open nozzle.<ref>{{cite book|last1=Warren|first1=J. W.|title=Understanding force: an account of some aspects of teaching the idea of force in school, college and university courses in engineering, mathematics and science|date=1979|publisher=Murray|location=London|isbn=978-0-7195-3564-2|pages=[https://archive.org/details/understandingfor0000warr/page/28 28–29]|url=https://archive.org/details/understandingfor0000warr/page/28}}</ref>]]
In other words, if one body exerts a force on a second body, the second body is also exerting a force on the first body, of equal magnitude in the opposite direction. Overly brief paraphrases of the third law, like "action equals [[Reaction (physics)|reaction]]" might have caused confusion among generations of students: the "action" and "reaction" apply to different bodies. For example, consider a book at rest on a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is ''not'' the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth.{{refn|group=note|See, for instance, Moebs et al.,<ref>{{cite book|first1=William |last1=Moebs |display-authors=etal |title=University Physics, Volume 1 |chapter=5.5 Newton's Third Law |chapter-url=https://openstax.org/books/university-physics-volume-1/pages/5-5-newtons-third-law |publisher=OpenStax |isbn=978-1-947172-20-3 |year=2023 |page=220}}</ref> Gonick and Huffman,<ref>{{cite book|first1=Larry |last1=Gonick |author-link1=Larry Gonick |first2=Art |last2=Huffman |title=The Cartoon Guide to Physics |year=1991 |isbn=0-06-273100-9 |publisher=HarperPerennial |page=50}}</ref> Low and Wilson,<ref>{{Cite journal|last1=Low|first1=David J.|last2=Wilson|first2=Kate F.|date=January 2017|title=The role of competing knowledge structures in undermining learning: Newton's second and third laws|url=http://scitation.aip.org/content/aapt/journal/ajp/85/1/10.1119/1.4972041|journal=[[American Journal of Physics]] |language=en|volume=85|issue=1|pages=54–65|doi=10.1119/1.4972041|bibcode=2017AmJPh..85...54L |issn=0002-9505}}</ref> Stocklmayer et al.,<ref name="Stocklmayer">{{Cite journal|last1=Stocklmayer|first1=Sue|author-link1=Susan Stocklmayer |last2=Rayner|first2=John P.|last3=Gore|first3=Michael M.|date=October 2012|title=Changing the Order of Newton's Laws—Why & How the Third Law Should be First|url=http://aapt.scitation.org/doi/10.1119/1.4752043|journal=[[The Physics Teacher]] |language=en|volume=50|issue=7|pages=406–409|doi=10.1119/1.4752043|bibcode=2012PhTea..50..406S |issn=0031-921X}}</ref> Hellingman,<ref>{{Cite journal|last=Hellingman|first=C.|date=March 1992|title=Newton's third law revisited|url=https://iopscience.iop.org/article/10.1088/0031-9120/27/2/011|journal=[[Physics Education]] |volume=27|issue=2|pages=112–115|doi=10.1088/0031-9120/27/2/011|bibcode=1992PhyEd..27..112H |s2cid=250891975 |issn=0031-9120}}</ref> and Hodanbosi.<ref>{{Cite web|url=https://www.grc.nasa.gov/www/k-12/WindTunnel/Activities/third_law_motion.html#:~:text=DESCRIPTION:+A+set+of+mathematics,with+Newton%27s+Laws+of+Motion.&text=The+book+lying+on+the,the+book+remains+at+rest.|title=Third Law of Motion|website=www.grc.nasa.gov |first=Carol |last=Hodanbosi |editor-first=Jonathan G. |editor-last=Fairman |date=August 1996}}</ref>}}

Newton's third law relates to a more fundamental principle, the [[conservation of momentum]]. The latter remains true even in cases where Newton's statement does not, for instance when [[Force field (physics)|force fields]] as well as material bodies carry momentum, and when momentum is defined properly, in [[quantum mechanics]] as well.{{refn|group=note|See, for example, Frautschi et al.<ref name=":0" />{{rp|356}}}} In Newtonian mechanics, if two bodies have momenta <math>\mathbf{p}_1</math> and <math>\mathbf{p}_2</math> respectively, then the total momentum of the pair is <math>\mathbf{p} = \mathbf{p}_1 + \mathbf{p}_2</math>, and the rate of change of <math>\mathbf{p}</math> is <math display="block">\frac{d\mathbf{p}}{dt} = \frac{d\mathbf{p}_1}{dt} + \frac{d\mathbf{p}_2}{dt}.</math> By Newton's second law, the first term is the total force upon the first body, and the second term is the total force upon the second body. If the two bodies are isolated from outside influences, the only force upon the first body can be that from the second, and vice versa. By Newton's third law, these forces have equal magnitude but opposite direction, so they cancel when added, and <math>\mathbf{p}</math> is constant. Alternatively, if <math>\mathbf{p}</math> is known to be constant, it follows that the forces have equal magnitude and opposite direction.