In this blog here, I tried to explain Newton’s 1st law of motion, the so-called *law of inertia*. Then, the following week, in this blog here, I tried to explain Newton’s 2nd law, the one with the equation , which tells us how a body accelerates if there is a (resultant) force applied to it. This week, I will finish up this series by trying to explain Newton’s 3rd law.

His 3rd law is very important. Without it cars wouldn’t work, we wouldn’t be able to walk forwards and rockets wouldn’t work in space. The 3rd law is often stated as *“to every action, there is an equal and opposite reaction”*. Another way of saying this is that, if you push on something, it will push back. It is the reason you get a recoil from a gun when it fires a bullet. The explosion of the bullet propels the bullet forward, and an equal force propels the gun back into your shoulder.

You might be asking yourself “hang on, the gun doesn’t come back at the same speed as the bullet goes out of the front, so how can it be equal and opposite?”. Well, remember it is the *force* which is equal and opposite. Force is mass multiplied by acceleration (Newton’s 2nd law), and the gun is many times more massive than the bullet. This means that the force applied to the bullet produces much more acceleration than the equal force applied to the gun, so the gun moves back much more slowly than the bullet goes out of the front (thankfully!).

When we walk, we are actually using Newton’s 3rd law to move ourselves forward. We push our foot onto the ground, but also slightly backwards (the difference between walking and just standing). The backwards push of our foot leads to the ground pushing us forwards. Try walking on slippery ice, and you quickly realise that it doesn’t work too well when friction is reduced and your foot slides as you try and push backwards on the ground.

A rocket moving through *empty* space is an example of Newton’s third law which often confuses people. This is because people don’t see *what* the rocket is pushing against. The answer is – *nothing*! But that does not mean there isn’t an equal and opposite reaction. The rocket sends gasses out of the back of the rocket through burning fuel (essentially a controlled explosion), and in pushing the fuel out of the back the equal and opposite reaction to this push is that the rocket is pushed in the opposite direction, forwards. The gasses coming out of the back do not need to be pushing against anything, the mere act of their coming out of the back means the 3rd law reaction is to push the rocket forwards.

So, that is it. With these three laws of motion, which Newton outlined in his 1687 masterpiece *The Principia* (which I blogged about here), the foundations of mechanics had been laid down. These foundations are still in use today, more than 300 years later. Despite Einstein showing that Newton’s laws of motion have their limitations (written in its simple form, Newton’s 2nd law of motion is not entirely correct), we still use them on a daily basis because we so rarely experience the situations where *relativistic mechanics* is needed.