Momentum Explained: Conservation, Collisions & Calculations

In today's video, we're going to look at momentum, which is a property that all moving objects have.

The main thing to know is that momentum is equal to the mass of an object multiplied by its velocity.

So, if we saw a 4 12,000 kilo dinosaur charging at 12 m/s, then it momentum would be 4,500

* 12. So, 54,000 kg m/s.

Whereas if we had a 1200 kilo car traveling at 25 m/s, then its momentum would be 1,200 * 25.

So 30,000 kg m/s. An important thing to remember though is that momentum is a vector quantity.

So it has both a magnitude and a direction. So here if we consider the forward

direction to be to the right then the dinosaur will have a positive momentum but the car must have a negative

momentum. The next thing to know is the conservation of momentum principle which

is the idea that in a closed system the total momentum before an event like a collision is exactly the same as the

total momentum after the event. To see how this works, let's imagine our dinosaur and our car as two particles

which are traveling towards each other and are going to collide after which they'll both continue moving together at

the same speed. How would we find their velocity after the collision?

Well, the first thing we need to do is find their total momentum before the collision, which we can do by adding

together the dinosaurs and the cars momentum. So, 54,000 plus -30,000,

which gives us positive 24,000 kg m/s. Then because of our conservation of momentum principle, we know that once

they've collided, their total momentum must still be positive 24,000. And remember that in this scenario, a

positive number means that it's going to the right. So after our particles collide together, they'll both get

carried to the right because the brown one had more momentum. And because they're both moving

together, we can now treat them as a single large particle. So to work out their shared velocity,

all we have to do is rearrange our momentum equation to show that velocity equals momentum divided by mass and then

plug in the values for this combined particle. So 24,000

divided by their combined masses from before, which would be 4,500 for the dinosaur plus 1,200 for the car. So

5,700 kilos, which gives us a velocity of 4.4 m/s to the right. So basically, after the dinosaur and the

car collide, they both continue moving to the right at a velocity of 4.4. 4 m/s.

Now, in some circumstances, the momentum before an event might be zero, like it is for stationary objects, which

don't have any momentum because they're not moving. And so, in these cases, the total

momentum after the event must also be zero. For example, if we imagine a gun before

it's fired, then its initial momentum would be zero because its velocity is zero.

However, once the gun fires, the bullet that flies out will have a momentum in the forward direction.

And so to compensate for this, the gun has to recoil backwards with an equal momentum so that together the total

momentum is still zero. So, if we knew that this gun had a mass of 2 kilos and that a 5 g bullet was

fired out at a velocity of 120 m/s, we should be able to work out the velocity of the gun's recoil.

The key to this is remembering that the gun's momentum plus the bullet's momentum must equal zero because it

started off at zero before the gun fired. The first thing we want to do is find

the bullet's momentum using this bottom equation. So we do 0.5 which is its mass in kilos

times its velocity of 120 which will give us a momentum of 0.6 kilome/s. Next we want to try and find the gun's

momentum. So again we just do the mass of 2 times the velocity but because we don't know what the velocity is yet we

can just write V for velocity. So the momentum will be 2 V where 2 is the mass in kilos and V stands for the gun's

velocity which we're about to find out. Finally, we can use these momentum values for the gun and the bullet to

rewrite our equation as 2V plus 0.6 equals 0. And then we can just rearrange this

equation to find out the missing value of V. So first we subtract 0.6 from both sides

giving us 2V =0.6 six. And then we divide both sides by 2, leaving us with V =0.3

m/s, which is the gun's recoil velocity. And remember, the fact that it's negative means that it's effectively

going backwards. Or in other words, it's going in the opposite direction to the bullet.

The one thing we haven't mentioned yet is that you need to know that the letter symbol for momentum is row which looks

like a P. So the momentum equation can also be written as P= MV. If you haven't heard yet, you can find

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