Conservation of linear momentum

Momentum is the mass times the velocity of an object. Here comes a billiard ball. What happens when it hits another billiard ball head on? Hmmm the first ball stopped and the second moved away instead. With the same velocity.

So, what happened? The Momentum of the first ball has been transferred to the other. Before they interacted only the first ball moved, and after, only the other. So Momentum can be transferred from one object to another! When one ball stops, the momentum of that ball has decreased.

The Momentum of the other ball increases, and it moves off... ... with the same velocity the first ball had. How much of the Momentum is transferred? Let's look at how much momentum the two balls have together. The masses of the balls are equal.

Momentum is equal to an object's mass times its velocity. This means that the Momentum of a ball when standing still is zero. The velocity of the first ball - before the collision - is equal to the velocity of the second ball - after the collision. Let's look at the momentum of both balls added together: The total momentum... is equal before and after the collision.

The velocity of the first ball has decreased as much as the velocity of the second ball is increased. Hence the Momentum of first ball decreased the same amount that the Momentum of the second ball increased. The total momentum is preserved. But how? Change in momentum is Impulse.

And impulse can be written: "Force" times "time". When an impulse happens during a short period of time, as in this case, in physics, this is called a collision. Let's look at "force" and "time" in this case. When the first ball collides with the second ball it affects it with a force. Newton's Third Law says the second ball consequently, will also affect the first ball with a force...

equal in magnitude... in the opposite direction. OK. That was the forces involved. What about the time?

Well, the balls are colliding during an exactly equal time. So long as they are both in contact they are both colliding with each other, right? Two Forces equal in magnitude in opposite directions acting during an equal amount of time. If we look at both balls together, the impulse in one direction is exactly the same magnitude as the impulse in the other direction. And the direction is exactly opposite.

Hence the total impulse of the two balls is equal to... zero. Impulse is the change in Momentum. And hence the total Momentum does not change. The momentum is conserved.

This is the Law of The Conservation of Linear Momentum. The total momentum before the collision is equal to the total momentum after the collision. Let's watch Kim and Jenny! Kim catches up with Jenny and holds onto her. They continue forward, but at a different velocity.

The Law of Conservation of Linear Momentum states that the total linear momentum before the collision is equal to the total linear momentum after the collision. The momentum is the mass times the velocity of an object. The mass times velocity of Kim plus the mass times velocity of Jenny is equal to their combined mass times their common velocity after the collision. They have the same mass "M", and Kim arrives with three times the velocity of Jenny. What velocity will they have after the collision?

Pause the film, and see if you can solve it on your own. The Law of Conservation of Linear Momentum states that the total momentum before the collision is the same as the total momentum after the collision So P before the collision is: "M" times "three V" plus "M" times "V" equals "four M V" The mass after the collision is equal to two M Then the velocity after must be equal to: "four M V" over "two M". That's "two V" Together, they're now moving slower than Kim was, but faster than Jenny was, before the collision. The Law of The Conservation of Linear Momentum: The total momentum before the collision is equal to the total momentum after the collision.