Editing Motion (section)

== Laws of motion ==
In physics, the motion of {{plainlink|url=//en.wiktionary.org/wiki/massive#:~:text=(physics%2C%20of%20a%20particle)%20Possessing%20mass.|name=massive}} bodies is described through two related sets of [[scientific law|laws]] of mechanics. [[Classical mechanics]] for super atomic (larger than an atom) objects (such as [[car]]s, [[projectile]]s, [[planet]]s, [[Cell (biology)|cells]], and [[human]]s) and [[quantum mechanic]]s for [[atom]]ic and [[subatomic particle|sub-atomic]] objects (such as [[helium]], [[protons]], and [[electrons]]). Historically, Newton and Euler formulated [[Newton's laws of motion|three laws of classical mechanics]]:
{| class="wikitable"
|First law:
|In an [[inertial reference frame]], an object either remains at rest or continues to move in a straight line at a constant [[velocity]], unless acted upon by a [[net force]].
|-
|Second law:
|In an [[inertial reference frame]], the vector [[Vector sum|sum]] of the [[forces]] F on an object is equal to the [[mass]] ''m'' of that object multiplied by the [[acceleration]] a of the object: <math>\vec{F} = m\vec{a} </math>.
If the resultant force <math>\vec{F}</math> acting on a body or an object is not equal to zero, the body will have an acceleration <math>a</math> that is in the same direction as the resultant force.
|-
|Third law:
|When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction onto the first body.
|}

=== Classical mechanics ===
{{Main|Kinematics}}
Classical mechanics is used for describing the motion of [[macroscopic]] objects moving at speeds significantly slower than the speed of light, from [[projectiles]] to parts of [[machinery]], as well as [[astronomical objects]], such as [[spacecraft]], [[planets]], [[star]]s, and [[Galaxy|galaxies]]. It produces very accurate results within these domains and is one of the oldest and largest scientific descriptions in [[science]], [[engineering]], and [[technology]].

Classical mechanics is fundamentally based on [[Newton's laws of motion]]. These laws describe the relationship between the forces acting on a body and the motion of that body. They were first compiled by [[Isaac Newton|Sir Isaac Newton]] in his work ''[[Philosophiæ Naturalis Principia Mathematica]]'', which was first published on July 5, 1687. Newton's three laws are:
# A [[Physical body|body]] at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force. (This is known as the law of [[inertia]].)
# Force (<math>\vec{F}</math>) is equal to the change in momentum per change in time (<math> \frac{\Delta m\vec{v}}{\Delta t}</math>). For a constant mass, force equals mass times acceleration (<math>\vec{F} = m\vec{a} </math> ).
# For every action, there is an equal and opposite reaction. (In other words, whenever one body exerts a force <math>\vec{F}</math> onto a second body, (in some cases, which is standing still) the second body exerts the force <math>-\vec{F}</math> back onto the first body. <math>\vec{F}</math> and <math>-\vec{F}</math> are equal in magnitude and opposite in direction. So, the body that exerts <math>\vec{F}</math> will be pushed backward.)<ref>Newton's "Axioms or Laws of Motion" can be found in the "[[Mathematical Principles of Natural Philosophy|Principia]]" on [https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA19 p. 19 of volume 1 of the 1729 translation] {{Webarchive|url=https://web.archive.org/web/20150928021402/https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA19 |date=2015-09-28 }}.</ref>

Newton's three laws of motion were the first to accurately provide a mathematical model for understanding [[orbit]]ing bodies in [[outer space]]. This explanation unified the motion of celestial bodies and the motion of objects on Earth.

=== Relativistic mechanics ===
Modern kinematics developed with study of [[electromagnetism]] and refers all velocities <math>v</math> to their ratio to [[speed of light]] <math>c</math>. Velocity is then interpreted as [[rapidity]], the [[hyperbolic angle]] <math>\varphi</math> for which the [[hyperbolic tangent function]] <math>\tanh \varphi = v \div c</math>. [[Acceleration]], the change of velocity over time, then changes rapidity according to [[Lorentz transformation]]s. This part of mechanics is [[special relativity]]. Efforts to incorporate [[gravity]] into relativistic mechanics were made by [[W. K. Clifford#Premonition of relativity|W. K. Clifford]] and [[Albert Einstein]]. The development used [[differential geometry]] to describe a curved universe with gravity; the study is called [[general relativity]].

=== Quantum mechanics ===
[[Quantum mechanics]] is a set of principles describing [[Physical systems|physical reality]] at the atomic level of matter ([[molecule]]s and [[atom]]s) and the [[subatomic particle]]s ([[electron]]s, [[proton]]s, [[neutron]]s, and even smaller [[elementary particle]]s such as [[quark]]s). These descriptions include the simultaneous wave-like and particle-like behavior of both [[matter]] and [[radiation]] energy as described in the [[wave–particle duality]].<ref>{{Cite web |url=https://feynmanlectures.caltech.edu/I_38.html |title=The Feynman Lectures on Physics Vol. I Ch. 38: The Relation of Wave and Particle Viewpoints |access-date=2022-05-03 |archive-date=2022-08-14 |archive-url=https://web.archive.org/web/20220814175040/https://www.feynmanlectures.caltech.edu/I_38.html |url-status=live }}</ref>

In classical mechanics, accurate [[measurement]]s and [[prediction]]s of the state of objects can be calculated, such as [[Absolute location|location]] and [[velocity]]. In quantum mechanics, due to the [[uncertainty principle|Heisenberg uncertainty principle]], the complete state of a subatomic particle, such as its location and velocity, cannot be simultaneously determined.<ref>{{Cite web |title=Understanding the Heisenberg Uncertainty Principle |url=https://www.thoughtco.com/the-heisenberg-uncertainty-principle-2699357 |access-date=2022-05-10 |website=ThoughtCo |language=en |archive-date=2022-05-10 |archive-url=https://web.archive.org/web/20220510035843/https://www.thoughtco.com/the-heisenberg-uncertainty-principle-2699357 |url-status=live }}</ref>

In addition to describing the motion of atomic level phenomena, quantum mechanics is useful in understanding some large-scale phenomena such as [[superfluidity]], [[superconductivity]], and [[biological system]]s, including the function of [[Olfactory receptor|smell receptors]] and the [[protein structure|structures of protein]].<ref>{{cite web|url=https://www.discovermagazine.com/the-sciences/how-quantum-mechanics-lets-us-see-smell-and-touch| title=How Quantum Mechanics Lets Us See, Smell and Touch: How the science of the super small affects our everyday lives| work=Discovery Magazine| date=October 23, 2018| last=Folger| first=Tim| access-date=October 24, 2021| archive-url=https://web.archive.org/web/20210126120506/https://www.discovermagazine.com/the-sciences/how-quantum-mechanics-lets-us-see-smell-and-touch| archive-date=January 26, 2021}}</ref>