# Momentum

**Momentum** is a vector quantity used to quantify an object's motion in which the direction of the vector is the same as the direction of the object and the magnitude is equal to the mass times the velocity. According to the law of conservation of **momentum**, in collisions between multiple objects, the total momentum of the system remains unchanged. The formula for momentum is *momentum = mass x velocity*.

Momentum, momentum is the mass of an object times its velocity. We've probably noticed if you have ever seen a large object and a small object moving towards each other that the large object is usually going to knock that small object back right? Because that's because the large object has more momentum okay, this is important when we're talking about collisions of vehicles or collisions of football players on a football field the object with a larger momentum is going to carry out, is going to move the other object. So let's, the units we use for momentum are again kilograms the unit for mass and meters per second the unit for velocity. Okay, so let's look at an example of a problem with momentum, okay again football players might like this I've got a football player running right towards the goal line and he weighs 100 kilograms right which is about 220 pounds that's a big fall back okay.

Here's my goal line okay and I've got this defender coming at him, the defender is not quite as big. And he wants to stop him at the goal line to prevent a touchdown. So the mass of the defender is 75 kilograms okay. If they're running at the same velocity, what's going to happen? Okay I'm sorry the same speed right and velocity is a directional so running at the same speed in the opposite direction. This guy has got more momentum and he's going to end up in the end zone, touchdown. Okay, so this guy has got to run a little faster than this guy okay? So let's see how we would calculate that okay.

In order to stop the runner, the runner would have to have no velocity right, no momentum okay at the goal line right? Because no matter how big an object is if it has no velocity, it has no momentum okay, so we want to get 0 kilograms times meters squared okay that's 0 momentum and that's going to equal our running back right 100 kilograms and his velocity 6 meters per second plus our defender which is 75 kilograms and we want to figure out what the velocity of the defender is in order to equalize the momentum of the object coming at him, the larger player. Okay so if we solve this we get 0 equals 600 kilograms meters squared that's our unit for momentum plus 75 v okay and again if we cancel, divide by 75 kilograms and if I got my units here okay. And I divide this by 75 kilograms okay I'm going to get my 0 momentum equals 600 divided by 75 is 8 and my mass cancels so 8 meters per second plus v. So in order for something to equal, cancel out to equal 0 my velocity must be minus 8 meters per second in other words the velocity in the opposite direction as the velocity coming up. So that would cancel out, so this person would have to be running 2 meters per second faster than the larger individual and they would have the same momentum. Okay, so this is how you can calculate momentum simply looking at the velocity of an object times the mass of the object. That's the objects total momentum.

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