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 four and a half thousand kilo dinosaur charging at 12 meters per second then its momentum would be 4 500 times 12. so 54 000 kilogram meters per second whereas if we had a 1200 kilo car traveling at 25 meters per second then its momentum would be 1200 times 25 so 30 000 kilogram meters per second 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 car's momentums so 54 000 plus negative 30 000 which gives us positive 24 000 kilograms meters per second 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 purple 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 four thousand five hundred for the dinosaur plus twelve hundred for the car so five thousand seven hundred kilos which gives us a velocity of four point four meters per second to the right so basically after the dinosaur and the car collide that both continue moving to the right at a velocity of 4.4 meters per second 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 gram bullet was fired out at a velocity of 120 meters per second 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 0.005 which is its mass in kilos times its velocity of 120 which will give us a momentum of 0.6 kilometers per second next we want to try and find the gun's momentum so again we just do the mass of two 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 two v where two 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 equals negative 0.6 and then we divide both sides by 2 leaving us with v equals negative 0.3 meters per second 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 equals m v that's everything for this video though so i hope you enjoyed it if you did then give us a like and subscribe and we'll see you next time