[MUSIC] This week, we'll keep going with momentum. Once we've defined momentum, we'll see another useful way of writing Newton's second law. And also another conservation law. Momentum is helpful in analyzing collisions, like this one, and we'll look at the analysis I made before I did the experiment to make sure it was safe. So let's introduce momentum. Momentum has the symbol p, and we define it as mass times velocity, m v. It units are kilogram meters per second. Momentum is a vector, parallel to the velocity. Double the mass, double momentum. Double the velocity, also double the momentum. Lets do a calculation to get used to the units and the magnitudes of momentum. So there's a point to remember. Mass and velocity contribute equally to momentum, but velocity is much more important in kinetic energy. Isaac Newton called momentum the quantitas motus, or in English, the quantity of motion. And he used momentum to write a more general form of his second law of motion. In modern notation we'd write it as total force equals change in momentum over change in time. Once again, Newton's third law tells us that the internal forces add to 0. So we have total external force equals change in momentum over change in time. Let's now check that this reduces to the form of the second law that we saw previously. Provided that the mass is constant, we have delta p equals m delta v. And we recognize the change in velocity over the change in time as the acceleration. So yes, this includes the version of the second law that we saw before, and, by the way, it also gives Newton's first and third laws. We'll give you a link for that. We use momentum to analyze collisions. In these multiple collisions, momentum is transferred from the ball at one end, to that at the other. [NOISE] The change in momentum transferred during interaction is called the impulse. Looking at Newton's Second Law, we can see that the impulse or change in momentum equals the average force times the duration. Or in the calculus version the integral of Fdt. If the impulse is just equal to the change in momentum, why do we bother with the name impulse? Well the answer is that usually we think of momentum as the property of a body in motion. Whereas impulse is what give to it if you collision. We need both of those, momentum and impulse, in this next bit. Here's that important equation. Newton's second law using momentum. And from it, here's another important result. Multiply both sides by delta t and we have change in momentum equals total external force times the time over which it acts. By the way, you should remember that change in momentum is force times time, and contrast that with work, which is force times distance, if they're parallel, but back to our equation. Change in momentum equals total external force times the time over which it acts. We can now say if the total external force is 0, then there is no change in momentum. And that means that momentum is conserved. In practice, we don't actually need the external forces to be 0. If the impulse do to the external forces is negligible, then momentum is conserved. Well to that approximation. I want you to be really careful about Conservation of momentum, and the condition under which it applies. For instance, my momentum is not conserved. Look, it's 100 kilogram meters per second north. It's zero. 100 kilogram meters per second south. Zero, north, zero, it's not conserved. That's because there's an external force acting on me, and so when I accelerate east, the Earth accelerates west. Though not very much because its mass is very much greater. Well, that's quite a bit to think about. So let's do a quiz before we go any further. And here's the first question. In the action of this pendulum cradle is momentum ever conserved and if so where and when?