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<   No. 2459   2009-10-20   >

1 Edmond Halley: Mr Newton, you really should have attended the theatre with me yesterday to take in the pantomime play.
2 Edmond Halley: As each character appeared, the children would cheer or boo! Then a rival character would appear and they would all make the other noise!
3 Edmond Halley: I suppose you could say that for each actor there was an equal and opposite re-actor.
3 Isaac Newton: Hmmm...
4 Edmond Halley: That Shakespeare really is a genius of children's literature.

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And so we reach Newton's Third Law of Motion, often expressed in simple terms like this:

For every action, there is an equal and opposite reaction.
The full formulation is a bit more complicated, but really that covers the essence of it. What it means is that forces are reciprocal interactions. You cannot exert a force on something without feeling a reactive force in the opposite direction. If you push against something, it pushes back at you - whether it's a person or just a brick wall.

It may sound odd that a brick wall can push back at you if you push it. But try this simple experiment: Stand with your toes touching a wall. Now, with your hands, push hard against the wall. Try to keep your feet still. (But not too hard - I don't want you injuring yourself!)

What happened? There was a force pushing you away from the wall. It wasn't the push you gave to the wall, because you exerted a force towards the wall. The force pushing you away from the wall is the reactive force, equal and opposite to your push towards the wall.

Here's something else to think about. When you walk, which direction do your feet push? If you don't think about it at all, you might be tempted to say "in the direction you're walking". After all, something must be pushing you in that direction, and your feet are the only things obviously providing the forces needed to to move your body.

But think about what your feet are actually doing to the ground. You plant your foot, and then your foot tries to push the ground backwards. This is easy to see if you imagine walking and accidentally stepping on a skateboard. Which way does your foot propel the skateboard? Backwards, not forwards. So your feet are definitely pushing backwards. Newton to the rescue! Your feet provide a force to the Earth, which means the Earth provides an equal force to your body, in the opposite direction. The entire Earth being pretty difficult to move, the result is that its reaction force pushes you forwards, rather than you pushing the Earth backwards*. When you walk, your feet are pushing backwards, and it's only through the magic of Newton's Third Law that you get where you want to go.

* Actually, there's a slight wrinkle here. In fact, you are pushing the Earth backwards when you walk. But because it's so much more massive than you, it moves a correspondingly smaller distance. Hey, why don't we do the calculation?

Let's assume for simplicity your mass is 100kg (a heavy man) and you step 1 metre per stride. The mass of the Earth is about 6×1024kg. So the distance the Earth moves when you take a step is approximately 100/(6×1024), or 1.7×10-23 metres. This is about 10-13 times the size of a hydrogen atom (a ten-trillionth, using the American definition of trillion). So not exactly enough to be noticeable. What's more, on average there will be approximately the same number of people all over the world walking in opposite directions over the course of a day, so the motion will tend to cancel out.

2023-07-13 Rerun commentary: If you really want to break your brain, try to imagine a world in which Newton's Third Law wasn't true. Replace it with anything you can think of, and imagine what life would be like.

It's a difficult exercise, and if you really think it through, you realise just how wacky things would be.

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