Intro to momentum (& it's meaning)

- [Instructor] A 50,000 kilogram plane is moving uncontrollably at one meter per second, and from the other side, a 2000 kilogram car is coming in, again, uncontrollably at 30 meters per second. They are both on a collision course. What's gonna happen? Well luckily, both Superman and Batman happen to be nearby, so they can go in and save the day. But the question is who should stop what? I mean, it's no secret. We all know Superman is stronger than Batman, right? No offense, Bats. And so it'll make a lot of sense to assign the harder task to Superman. And that's exactly what we need to figure out in this video. We need to find out in which case it's gonna take more efforts to stop: the plane or the car. So, what do you think? Which is harder to stop? Well, at first we might say, look, the plane is so much heavier compared to the car, and so stopping the plane is going to be difficult. I mean, you might know the heavier something is, more difficult it is to stop. For example, if I threw a bowling ball at you, I won't do that, don't worry, but if I did, it's harder to stop compared to if I threw a ping pong ball at you, right? And so that way we can say because this is more massive, it's harder to stop. But on the other hand, if you look at the car, that car is way faster than the airplane. It's going at 30 meters per second, and to give you some context, if you convert that into kilometers per hour, it's over 100 kilometers per hour. That is pretty fast. And you might know that if something is super fast, even then it's hard to stop, right? For example, that's why bullets are very hard to stop because they are light, but they are pretty fast. So, how do we decide? It seems as if the effort needed to stop something depends on both of these things. It depends on the mass of an object and it also depends on the speed of that object. And so, it turns out that in reality, the efforts needed depend on the product of the mass and the velocity. All right? So, we come up with a new quantity for this purpose where we multiply the mass of the object with the velocity of the object. It's this number that tells us how much efforts are needed to stop that object. And we give a name to this number. We call this momentum. We call this as the momentum of the object and the symbol used for momentum is P because M is already taken. And so, I like to think of momentum as a number that tells us how hard it is to stop something, which means more momentum, harder it is to stop an object. Of course it turns out there are other ways to think of momentum and we will talk about them in other videos, but in this video we'll just stick to this. Now, before we go ahead and calculate the momentum of these bodies and answer our question, let's get a little bit more feeling for this formula. This says that if the velocity of the object is zero, its momentum goes to zero. Does that make sense? Well, it does, right? If something has zero velocity, it means it's not moving at all. And if it's not moving at all, it doesn't take any efforts to stop, and so it makes sense to say its momentum is zero, okay? What about if its mass is zero? Even then, the momentum goes to zero. Does that make sense? Well, yeah. Imagine something which has zero mass. Okay, that's hard to imagine. Imagine something which is very, very light. Say, very light compared to our body weight. Imagine a mosquito, okay? Let's say I take a tiny mosquito, all mosquitoes are tiny, let's say I take a mosquito and I threw it at you, okay? Threw it at you at some speed. How hard is it to stop that? Well, it's pretty easy, right? I mean, if I threw it at you, if it hits you, you wouldn't even feel it, right? It's super easy to stop that. And so, we could say that momentum of a mosquito is pretty much zero. Does that make sense? So if something has very small mass, it has very small momentum. That's what it means over here. On the other hand, imagine something which has both very high mass and high velocity. Now, it has super high momentum. Does that make sense? Well, yeah. I mean, imagine a freight train, which is very heavy, and let's say it's going at 100 kilometers per hour. Ooo. Can you imagine trying to stop that? That is gonna be super hard to stop, so it makes sense to say it has very, very high momentum. All right, another quick thing we'll do is figure out its units. In fact, can you try this? Can you think about what the units of momentum is gonna be? Just give it a shot. Okay, let's see. Mass has a unit of kilograms. Velocity has a unit of meters per second, so when you're multiplying that, even the units get multiplied. So it's gonna be kilograms meters per second. That's the unit of momentum. All right, and now comes the moment that we've been waiting for. We can go ahead and calculate the momenta of both of these objects. And by the way, momentum is singular, momenta is plural. So anyways, we can calculate the momenta of both of them and figure out which one is higher. Whichever is higher, that would be harder to stop. Now, I know you are super, super excited to do this, so why not give it a shot first. Pause the video, go ahead and calculate the momentum. All right, let's do this. So, let's first do the momentum of the airplane. I'm gonna call P-A, A for airplane. That's going to be the mass of the airplane, which is 50,000 kilograms. So, 50,000 kilograms times the velocity of the airplane. That's going to be one meter per second. And how much is that? Well that is 50,000 times one, that's just 50,000. 50,000. And the units are, notice I don't have to remember the units. I'll just look at this and I can multiply the units here itself. So, the units are going to be kilogram meters per second. Okay, let's do the car now. The momentum of the car, which we'll P-C, C for car, that's going to be mass of the car, which is just 2000 kilograms times the velocity of that car. That's gonna be 30 meters per second. And that will be, let's see how much that is. Two times three is six, one two three four, 60,000 kilogram meters per second. So, which one is higher? Well, it's the car. The car turns out to have a higher momentum. That means it'll take more efforts to stop that car. So even though the car was lighter, much lighter compared to the airplane, it is going so much faster that it turns out it takes more efforts to stop it. It has a higher momentum. And so, now we know what to do. Since the car is the one that's harder to stop, we can assign that to Superman. Batman gets the airplane and our day gets saved. And so, what did we learn in this video? We learned of a new quantity called momentum. We can think of it as a number which tells us how hard it is to stop something. More momentum, harder it is to stop. And we also learned how to calculate it. We calculate it as a product of mass and velocity.