Guys, in this video, I'm going to introduce you to a new physical quantity called momentum. We're going to be talking a lot about momentum in the next couple of videos, so it's a good idea to get a good conceptual understanding of what it is, how we calculate it, and also how we solve problems with it. Let's check this out. Momentum is really just a physical quantity that objects have. It's kind of like energy, and it's really just related to an object's mass and its velocity. So objects that have mass, that are moving with some velocity, have momentum. The equation for it or the letter that we use is lowercase 'p'. Don't ask me why. And it's really just \( m \times v \), \( p = m \times v \). Very straightforward.

So, let's talk about the units. The units really just come from these two letters, 'm' and 'v'. Right? The units for mass are kilograms, and the units for velocity are meters per second. So momentum actually doesn't have a fancy unit like a joule or a watt or a newton or anything like that. It's just kilogram meters per second. So if you ever forget, you can always just get back to it by using \( m \times v \).

Like I said before, we're going to be talking a lot about momentums and an object's momentum, how it gets changed or transferred, and so it's a good idea to get a good conceptual understanding of what it is. Momentum, conceptually, is really just a measure of how difficult it is to stop moving objects.

So let me back up for a second because we've talked about a similar idea which is inertia. Remember that inertia was how hard it is to change an object's speed. And if you remember, inertia was really just your mass. Mass is a measure of inertia. If you have lots of mass, or if you have like 100 kilograms, then you have to push really hard in order to change your speed versus if you had like 10 kilograms or something like that. So momentum is kind of related to inertia, except it only just applies to moving objects.

So really, if you look at the equation for momentum, there are actually two ways you can have lots of momentum. So you could have lots of mass, right, lots of inertia. Therefore, it's harder to stop you, but you could also have lots of speed, and it's also harder to stop you. Right?

So let me go ahead and actually work out this problem here, just so I can show you what I mean by this. So here we have a truck and a race car that are moving. So I'm going to draw this little flat surface like this. So I've got a 4000 kilogram truck, that's the mass, and it's moving to the right with some speed. So this is \( v_t \). I also have an 800 kilogram race car that's moving to the left with some \( v_r \).

What I want to do is I want to calculate the momenta. Right? This is just the plural word for momentum of both vehicles here. So I'm going to calculate \( p_t \) and then \( p_r \) just by using the equation here. So let's talk about the truck first. Well, if you think about this, the truck, right, really has some momentum because it has some mass and it's moving to the right. Now what I want to point out here is that momentum is actually a vector. We can see from the equation here that if you have \( p \), \( m \), and \( v \), what happens is that your velocity is an arrow. Right? That's a vector. And if your momentum depends on velocity, then momentum is also a vector and it just points in the same direction as your velocity.

So momentum is always going to point in the same direction as an object's velocity. So if you have an object moving to the right with some velocity, then its momentum is also going to be to the right like this. So when we calculate the momentum for the truck, we're really just going to use the mass of the truck times the velocity of the truck, which we know is equal to 10 meters per second. So what I'm going to do is I'm going to choose the right direction to be positive and, therefore, my velocity is going to be positive. So I'm just going to calculate. This is going to be 4000 times the velocity of 10, and I have the momentum is really just equal to 40000 kilogram meters per second.

So let's talk about the race car now. Now the race car is moving to the left, which means that it's actually going to have a negative velocity. We're told that the race car is 50 meters per second, so \( v_r \) is actually going to be negative 50 meters per second. Signs are going to be very important in these kinds of problems. So once you pick a direction of positive, you're going to stick to it. So what happens is if you have an object that's moving in the direction of negative, then the velocity and the momentum are both going to be negative here.

So \( v_r \) is negative 50, and when we calculate the momentum of the race car, we're just going to use the mass of the race car times the velocity of the race car. So this is going to be 800 times negative 50. So now when you work this out, the momentum of your race car is going to be negative 40000 kilogram meters per second.

So, notice how we got the same number and we also got a negative sign here. So if you take a look here, we actually have the same number that we calculated for the momentum of the truck versus the momentum of the race car. And, really, this just points out, I'm just trying to point out here that it's actually just as difficult to stop both of these moving objects here because they have the same magnitude momentum.

So for the truck, the truck has a high mass. Right? Its \( m \) is very high, but its speed is only 10 meters per second. It's not moving that fast. So the race car is actually much lighter. It's only 800 kilograms. The \( m \) isn't as high, but the speed is actually much greater than the truck's. So depending on, you know, so basically, between the two, it's actually just as difficult to stop the race car moving as it is to stop the truck.

Alright. So hopefully that makes sense, guys. Let me know if you have any questions.