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# Newton’s 3rd law (action/reaction)

• Hit the baseball with your bat,
• throw a bouncing tennis ball against a wall,
• crash your car into a tree, and
• punch a punching bag.

What do these scenarios have in common? Of course that they are all impacts. Or collisions. We might in general call them interactions.1 Interactions between two things (objects, particles etc.). In each impact scenario forces are of course being applied:

• The baseball flies back when you hit it,
• the tennis ball pushes on the wall2
• the crashing car breaks the tree in half, and
• the punching bag starts swinging.

But apart from what the impacted object feels, doesn’t the impacting objects feel something as well? Isn’t there a force both on the object being hit and on the hitter?

• Not only the baseball, but also the bat flies backwards,
• the tennis ball not only pushes on the wall but also bounces back itself,
• not only the tree but also the car breaks, and
• your hand gets sore and swollen after punching.

It seems that you can’t apply a force without feeling a force. We might say that ‘every action has a reaction’. Or that ‘every cause has an effect’. There is never just one force, there is always a force-pair.3

If we measure carefully, the reaction force turns out to always be exactly equal! Just opposite.[3,2,4] Meaning, the action-force and the reaction-force have the same magnitude but are in opposite directions.4 Let’s write this as:

$$\vec F_\text{A on B}=- \vec F_\text{B on A}$$

where $\text A$ and $\text B$ are the objects that interact. The negative sign here tells that the force vectors are exactly opposite. This is usually called Newton’s 3rd law,5 [3,4] and was originally phrased by Newton in this way:6

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.

Sir Isaac Newton[2]

This law is why an astronaut in space shouldn’t push on the outside space station wall; the wall will push back on him and he will drift off!

References:

1. Online Etymology Dictionary’ (dictionary), Douglas Harper, www.etymonline.com
2. Philosophiæ Naturalis Principia Mathematica’ (book, English translation published 1728), Isaac Newton, 1st ed., vol. 1, 1687, en.wikisource.org/wiki/Page:Newton%27s_Principia_(1846).djvu/89 (accessed Sep. 27th, 2019)
3. Sears and Zemansky’s Univesity Physics with Modern Physics’ (book), Hugh D. Young & Roger A. Freedman, Pearson Education, 13th ed., 2012
4. Equal & Opposite Reactions: Newton's Third Law of Motion’ (web page), Jim Lucas, Live Science, 2017, www.livescience.com/46561-newton-third-law.html (accessed Apr. 6th, 2020)