Newton's Third Law of Motion | Conservation of Momentum | IGCSE & O Level

A rifle fires a bullet at 800 metres per second. The rifle pushes the bullet forwards and the bullet pushes the rifle backwards just as hard, for exactly as long. So why does the rifle not come out of it at 800 metres per second too? Newton's third law and conservation of momentum, explained for IGCSE and O Level Physics. It takes one division. But first there is an argument to have, because most people do not accept the setup: a lorry hits a fly. Which pushes harder? Almost everybody says the lorry, and it is not a guess — it is built on evidence. The fly is squashed flat. The lorry is not damaged at all. If that is not a bigger force, what would be? Everything you saw is true. The step that fails is the next one, where you go from what you saw to what it means. You are judging the force by the damage, and damage is not force. It is what a force does to one particular object, and the two objects are not the same. The pushes are equal. Always — whichever is heavier, whichever is moving, whichever you think of as doing the hitting. So why is one destroyed? Because acceleration is force divided by mass — episode two. A loaded lorry is about 40 tonnes, a housefly about 12 milligrams. Same force, three billion times the mass. Put numbers on it. The lorry is doing 90 km/h — 25 m/s. The fly goes from rest to 25 m/s while being crushed through its own body length, 7 mm: that is 45 000 m/s², four and a half thousand g. Mass times acceleration gives about 0.54 N, the weight of a hen's egg on your hand. The same 0.54 N on 40 tonnes gives 0.000013 m/s². Equal forces, wildly unequal outcomes, both true at once. THE SECOND FACT, AND IT IS THE ONE NOBODY NOTICES When two things collide, how long does the push last? The same length of time, for both. The contact starts when they meet and ends when they part, and that is one length of time, not two. One shared t. That is the whole trick. Equal and opposite forces, acting for one shared time, give equal and opposite impulses. An impulse is a change of momentum, so the two changes are equal and opposite, and adding them cancels. Not the momenta, which is the trap. Not the forces, which are both still there on two different objects. The CHANGES cancel. One gains exactly what the other loses, so the total comes out of the collision exactly as it went in. That is the principle of conservation of momentum, and it is not a new law to learn. It is the third law multiplied by time. One condition, and the exam wants the phrase: nothing else may push on the pair from outside. An isolated system. Back to the rifle. Before the trigger nothing is moving, so the total momentum is zero, and after, it still has to be. The bullet is 4 grams at 800 m/s — 3.2 kg m/s forwards — so the rifle carries 3.2 kg m/s backwards. The rifle is 4 kilograms, and 3.2 divided by 4 is 0.8 m/s. Walking pace: a thousand times the mass, a thousandth of the speed. WHAT IS COVERED Newton's third law — conservation of momentum — impulse — momentum — Newton's second law — isolated system — recoil — rocket propulsion — collisions Every definition is in the wording examiners mark, with the common trap next to it. The two forces act on DIFFERENT objects, so they never cancel each other out. Momentum carries a direction, and that minus sign has to survive the arithmetic. And "equal and opposite" is only half an answer — the marks are in saying what is NOT equal. FIVE PLACES IT SHOWS UP A rocket in space, which brought something to push. Walking, where you push the Earth backwards and it pushes you forwards — and yes, the Earth moves. Two skaters pushing apart, where the lighter one leaves faster, not because they pushed harder but because they cannot. Two trolleys that stick together, the exam's favourite. And the fly. SOMETHING TO TAKE AWAY You run a 400 metre race, one lap, finishing where you started, in 50 seconds. Your average speed was 8 m/s. What was your average velocity? Answer in the comments. Chapters: 0:00 A rifle fires a bullet 0:16 Why the rifle does not come out at 800 m/s 1:50 A lorry hits a fly: which pushes harder? 2:26 Why everyone says the lorry 3:11 Damage is not force 3:58 Newton's third law, defined 4:29 So why is the fly squashed? 5:06 Putting a number on the fly 6:10 The force on each, and the accelerations 7:18 Equal forces, unequal outcomes 7:52 The second fact: one shared time 8:32 The proof: force x time, both sides 9:01 What cancels, and what does not 9:51 Conservation of momentum, defined 10:08 The isolated system 10:24 The rifle, answered 11:35 Why holding it tight helps 11:52 A rocket in space 12:16 Walking, and the Earth moves 12:42 Two skaters on ice 13:12 The exam's favourite: two trolleys 13:40 Back to the fly 14:05 What would change my mind 14:15 Something to take away 14:32 Next: velocity, properly defined Companion worksheet — exam-style questions with solutions: https://claude.ai/artifact/MYQWUWEAsC...