-as of [24 AUGUST 2025]-
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“IF 2 [BODIES] EXERT [FORCES] ON EACH OTHER, THESE [FORCES] HAVE THE SAME [MAGNITUDE] BUT OPPOSITE [DIRECTIONS]”
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Newton’s third law:
Newton’s third law is an odd beast because it was already violated by the discovery of magnetism.
In classical electromagnetism, moving charges do not obey Newton’s third law.
The way to patch it up is to replace Newton’s third law with the conservation of momentum
(and notice that electromagnetic fields have momentum.)
Conservation of momentum again survives into special relativity with no trouble, as long as you use relativistic momentum
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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
Rockets work by creating unbalanced high pressure that pushes the rocket upwards while exhaust gas exits through an open nozzle
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” 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
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 fields as well as material bodies carry momentum, and when momentum is defined properly, in quantum mechanics as well.[note 7] In Newtonian mechanics, if two bodies have momenta
p
1
{\displaystyle \mathbf {p} {1}} and p 2 {\displaystyle \mathbf {p} {2}} respectively, then the total momentum of the pair is
p
p
1
+
p
2
{\displaystyle \mathbf {p} =\mathbf {p} {1}+\mathbf {p} {2}}, and the rate of change of
p
{\displaystyle \mathbf {p} } is
d
p
d
t
d
p
1
d
t
+
d
p
2
d
t
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{\displaystyle {\frac {d\mathbf {p} }{dt}}={\frac {d\mathbf {p} {1}}{dt}}+{\frac {d\mathbf {p} {2}}{dt}}.}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
p
{\displaystyle \mathbf {p} } is constant. Alternatively, if
p
{\displaystyle \mathbf {p} } is known to be constant, it follows that the forces have equal magnitude and opposite direction.
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*👨🔬🕵️♀️🙇♀️*SKETCHES*🙇♂️👩🔬🕵️♂️*
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👈👈👈☜*-NEWTON’S 3 LAWS OF MOTION-* ☞ 👉👉👉
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💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥