This One Trick Will Teach You 3rd Law Of Motion

Textbooks don’t tell you this secret about Newton’s 3rd law of motion

Okay, what I’m about to tell you isn’t a secret, or well it really shouldn’t be but it’s the critical part of the 3rd law of motion that nobody says clearly or at least was not said clearly to me. And because of which most people don’t get the 3rd law of motion. And so I intent on delivering on my clickbait headline. But, first let’s get on the same page. Many textbooks , most likely yours, defined the 3rd law of motion as:

For every force called the action there is an equal and opposite force called the reaction

Simple, beautiful, elegant, and you think you’ve got it. Then you discuss a few examples. The examples are probably something like this:

1. You try to step off a boat and the boat slides back from the reaction and you fall into the water.
2. A rocket pushes back on the air and ground with thrust. It accelerates forward.
3. When you’re standing on the ground the gravity of the Earth pulls you, and the ground pushes you up

So far as good? If the answer is yes, then I’d like to welcome you to the club of people that have been fooled by their science classes. The examples I gave you are partially broken. For now trust me. First let me give you the secret. Action and reaction forces are always on two different objects. So let me restate the definition of the 3rd law of motion:

For every force called the action exerted from object A on object B there is an equal and opposite force called the reaction force exerted by object B on object A.

The frustration of a typical student studying. Also your frustration at me using a pure clickbait title // Photo by JESHOOTS.COM on Unsplash

And I’m sure you saw a lot of this in the examples you learned in school. But there were enough things said that kind of aren’t good examples if not completely misleading. And that’s why I wanted to write this article.

What We Know

There are four forces known in the world of Physics. These are:

1. Gravitational
2. Electromagnetic
3. Strong nuclear
4. Weak nuclear

These four forces exist in nature in pairs. For example when the Earth pulls you, you pull the Earth. When a proton pulls an electron, the electron pulls the proton. When an electron repels one electron, the second electron repels the first back. All forces we observe are these forces occurring Avogadro’s Numbers of times (Am I the only one that feels this should be a real expression). Well mostly the first two but I don’t know Physics enough to know if you would ever observe the latter two.

Aha, you say, how is my pushing an object one of these forces. Well, hate to break it to you but unless you’re a neutron you’ve never touched anything. The electrons in your hand have repelled the electrons on the object and vice versa. Also now that I’ve established that you’ve never touched anything in your life, I’m going to have to ask you to remember this moment and be okay with some things you’re experiencing intuitively are not reflective of reality.

What happens when you actually touch the nucleus of an atom // Public domain image courtesy of US Department of Energy with wiki article on Nuclear Weapon for helping find it.

It’s also worth remembering that the law of conservation of momentum is just a restatement of the 3rd law of motion. Because if there is an action force acting for some amount of time on one object in one direction, the reaction force will act on the same object in the opposite direction. It could be that there is something we don’t understand about forces that provides limits on the 3rd law of motion. But we don’t know of any such thing.

Also since I don’t want to sound like a sociopath I’m going to use the the word touch and push as we commonly understand them rather than mentioning the interatomic repulsion from the electron clouds of the atoms in our hand and other objects.

Learn To Walk

They always say learn to walk before you run. And learning to walk is a really good example. You have friction between your feet and the ground. You push back on the ground and as long as you don’t cross static limiting friction your foot stays in place and the force of the ground back on your foot that you transfer to the rest of the body propels your body forward.

Yes there are pairs of forces going all the way up the leg. Until the torso that actually moves forward.

So this is how the 3rd law of motion allows you to walk. And if you don’t have friction helping you providing the reaction force you have something like this:

What happens when you don’t have friction helping you propel yourself forward. As you’re looking at their struggles, notice how little the actual movement in the direction he’s trying to move in is.

Pushing An Object

With the example of walking we have an advantage because we have friction and it is easy to relate with what we observe in daily life. But now let’s consider the example of an object on physicists favorite surface, a frictionless surface. So you apply the force on the object? Where’s the reaction coming from? Well, from the same place as with friction. Your pushing the object is creating the reaction force back. Are you visualizing with me here? you’re pushing the reaction force is there, the object is getting faster, you’re keeping up and pushing faster your hand is moving faster, the object is getting faster you’re getting the reaction. Now earlier I said I’m going to ask you to suspend your intuition. Well, this is that moment. It is very easy to have your experiences misguide you here. Because you haven’t had many moments where you can perpetually accelerate. So you’ve only observed this for short intervals. But as long as you’re accelerating the object you will feel the reaction force.

One place where you can observe this is in rocketry. Mostly because it is easier to find frictionless surfaces in space. Now let me present to you a mostly scientifically inaccurate clip from a movie famous for being scientifically inaccurate.

The shuttles apply thrust. The thrust applies an action force causing an acceleration up to 9g’s on the astronauts. In return they push back into their chairs.

Rewatching, I’m not sure if I’ve helped the cause here or not. But another example would be when you gun your car. You will push against your carseat more as long as the car is accelerating. Once The car starts to hit max speed you won’t feel it pushing you and you won’t push it in return.

Revisiting The Boat

So why was the boat a very bad example. Let’s take an example of a small craft, let’s say a paddleboard that you are stepping off. Let’s say you weigh 9 times as much as the paddleboard. You instinctively know how fast you want to walk and you move your foot back at 1m/s. Except your foot is not pushing back on earth which is very massive. It is pushing back on a paddleboard that is on a very low friction surface and has 1/9th the mass of you. So the actual force that you apply is the force needed that you and the paddleboard are moving apart at 1m/s. Since the action and reaction forces are equal and opposite this translates to you moving forward at 0.1m/s and the paddleboard moving back at 0.9m/s.

You did not fall down because of a reaction force. You fell down because the action and reaction forces were 1/10th what you expected. So while you moved forward at 0.1m/s and the board moved

And so you’ve barely moved forward toward the dock and you’ve lost the platform you were standing on and hence you’re in the water. Did you fall into the water because of the reaction force, in the most technical of sense yes. Because both the forces are equal and opposite we can call either an action and a reaction. But it definitely feels silly calling the force in which you have agency as the reaction force because that is what pushed the boat back. And if you moved your foot fast enough (90m/s or 201mph fast enough) you could have still gathered enough force to propel yourself forward by 1m/s. If however, you were on a large ship that weighs 100s of times more than you. The amount you push the ship back would be negligible.

How Does Rocket Thrust Work

Well, for starters the rocket does not need the air or the ground for thrust. If it did, it wouldn’t work in space. So where is the third law of motion being applied? What are we applying the action on to get the reaction to propel us forward? We’re pushing gas particles back to propel ourselves forward. Let’s try to visualize it.

Now I can’t think through Avogadro’s Number of particles so let’s say we have two particles each of mass m. We have heated them up so now they’re moving extremely fast with velocity v. To get really fast they can just knock against each other and so they’re applying forces to each other. Now I had mentioned the law of conservation of momentum is equivalent to the 3rd law of motion because it means two objects always apply the same force on each other for the same amount of time. I’m going to cheat slightly because the force is applied for a very short amount of time. Now check out the diagram below

a) The particles are moving away from each other in a closed chamber. Since these particles are moving in equal and opposite directions right now we are in compliance with the law of conservation of momentum and the 3rd law of motion. Each has a momentum of mv in opposite directions. b) Shows the two particles hitting the opposite ends. Each of them hits the chamber wall and bounces back in the opposite direction. There was a force applied on the opposite walls of the chamber and they cancel each other out. This is observed as a pressure on the chamber walls. c) Shows a chamber with a wall removed. Same two particles are traveling away from each other with a momentum mv. d) The particle going right exits the chamber. The particle going left hits the wall and bounces back. In bouncing back it sees a change in momentum of 2mv from the force the wall applied on it. In return it applied the same force on the wall. This time the force is not canceled. And imparts a momentum of 2mv. Of course the chamber is a lot more massive and this same momentum is not going to get the same velocity as each particle but each of the particles hitting one wall and not getting its impact cancelled from the other side will apply a force to the rocket.

Please notice if we had launched the two particles directly with the momentum of mv we would have gotten 2mv momentum for the rocket. But what we showed was that we got the same behavior from just heating of the gas resulting in random motion and how we turned it into directed flow that gives you thrust.

Just Standing Around

So what was so broken about the example of standing around. Well, you know what to look for. In the description there are two forces acting on the same object. So the description is broken. The answer there are two pairs of forces. The pair of gravitational forces, and the force of pushing against the ground and back. I’ve drawn a diagram showing the forces.

The four forces at play. The pair of gravity forces. And the pair of forces from the pushing of your feet on the ground

This Seems Like A Change In Pace For You

You are correct. It is. And I wanted to pick on it because going with the theme of what I’ve been saying on this blog in we need to relook at how we do education. And this is something that was repeatedly taught. And a lot of people thought they got it. But the examples we’re provided lose the essence in finely tuned phrasing that the learner is not able to appreciate. And so many people end up missing the most significant part of something they’ve been taught. And they continue to miss this repeatedly.

Also I have to give credit to the Khan Academy. Their article on the 3rd law of motion actually makes it clear what needs to be said. Which both is a testament to the quality of material on Khan Academy and puts more questions on what sources deserve our trust.