 Conservation of momentum and conservation of energy are fundamental principles in physics and they apply relativity, quantum mechanics and everyday life. So when do you use one rather than the other? So our two conservation laws are conservation of energy and conservation of momentum. Now we're not going to prove this at the moment, but it turns out that the conservation of energy and conservation of momentum come from deeper principles. The conservation of energy actually comes from the idea that the laws of physics stay the same over time. And the conservation of momentum actually comes from the idea that laws of physics are the same in different places. So those are very deep principles that give us these conservation laws. That link we won't be able to make until university level physics, but for now let's look at just how we use these things. So conservation of energy is particularly useful to use because it's just one number. Energy is a scalar. And it has a lot of different forms, and so that means you can use it in very complicated situations sometimes. So you might have a roller coaster, and if you have someone on this roller coaster, and even though as they move along this roller coaster, they're going to have forces pointing in different directions due to the roller coaster pushing them away. They're going to have a constant force due to gravity pulling them down. That's going to turn into all sorts of complicated accelerations and so forth. But we know that we can use the conservation of energy because provided the friction between the trolley and the roller coaster is small, then that's not going to do any work. And so the energy it has at this point is going to be energy it has at any other point. And so if I want to know what speed it's going to say at some other point, I just look at the change in the potential energy and that's going to have been turned into kinetic energy. Now conservation of momentum would be a terrible thing to try and use for that problem because momentum is a vector quantity. And in this problem, the force of gravity and the force of the roller coaster pushing on it, the normal force, will be changing the momentum of this trolley all the time. And indeed it will be changing in different directions. I'm going to add up all the different changes of momentum in all those different directions as it goes along here to figure out its final velocity. So that would be an incredibly inefficient and hard way of doing this problem. But sometimes momentum is exactly the right kind of law to use. And the reason for that is that momentum only has one form. Whereby contrast, energy has lots of forms. What that means is if you have say a collision of some kind, supposing you have a road and there's a couple of cars and one car bangs into another, then the nice thing is that after the collision, no matter how mushed up these cars are, and no matter how many directions all the different pieces are going, we can still use the conservation of momentum because there's only one form of momentum. And it's always good to separate your before and after pictures very explicitly in your diagram. So I'll do that. Clarity in a diagram really stops you from getting confused and helps communicate what you're saying to other people as well. Anyway, we could have used energy or conservation of energy in this problem in some sense because we know that energy is conserved. If you have two things smashing together, energy doesn't disappear or appear. On the other hand, there's a lot of different forms of it. So there's the kinetic energy of all these pieces flying off, but there's also the potential energy required to change the shape of all those cars and rip bits off. Fundamentally, that's an electrical potential energy, but it's something we're not tracking, and so it's hard to use conservation of energy for this problem. Now in a collision like this where their total kinetic energy isn't conserved, it's called an inelastic collision. So of course everything conserves total energy, but not everything conserves kinetic energy. If a particular collision does happen to conserve kinetic energy, that's called an elastic collision. This is an elastic collision.