 Newton's second law. We saw in Newton's first law that he came up with the concept that forces cause changes in the motion. And a change in motion really means we're talking about a change in the velocity, or that delta v, meaning delta v and change in. Well, whenever I had a change in velocity, that was related to the acceleration. The acceleration was how fast the motion was changing. So what this really means is that Newton's first law implies that forces cause accelerations. Now his second law quantifies this. So Newton's second law states that the acceleration is proportional to the net force and inversely proportional to the mass. And again, we're translating this from Latin, so it's not an exact representation of what he said. Mathematically, we represent this by saying that the acceleration is equal to the force divided by the mass, so that it's directly proportional to the force and inversely proportional to the mass. We often see this equation rewritten just a little bit to rearrange the terms and give us our familiar f equals ma, where the net force is equal to the mass times the acceleration. So net force, let's talk about what that means here. If I have more than one force, I have to consider the net effect of all of the forces. If there's only one force, that is the net force, but if there's more than one, I need to take that into account. Now mathematically, we express this as the net force is the sum of however many forces I have acting on the system. If it's just one force, then the net force is that. If I've got two forces, I have to add those two forces together to find the net force. If I've got three forces, etc., regarding of how many forces I've got. Mathematically, this sum of however many forces I have is often written with the Greek uppercase sigma, and that's the summation symbol in mathematics. So the sum of all the forces is the same thing as the net force. Now you may have noticed in that previous equation that I had vectors in there. And see, forces are vectors. They have direction. It matters how hard I'm pushing or pulling, but also which direction. And that means I can represent those vectors as having components in the x direction and the y direction. And I could use my standard vector notation to write out that the force, the vector force, is the force in the x direction plus the force in the y direction, where I'm representing my directions by my i and j vectors. That means when I do the vector sum, I have to take into account their directions. Now you remember when we're doing the vector sums, it was easier to work with all the x's first and then all the y's, because we had to add up the i components and the j components separately. So I could express that as the sum of all the x components. I've got f1x plus f2x plus f3x, et cetera, however many x components I have. And that's going to give me the mass times the acceleration in the x direction. Do the same thing with the y components, and that gives me my y component of the acceleration. So each one of our forces, f1, f2, f3, however many I have, have both an x and a y component. And in the end, we have an acceleration that has x and y components. So both acceleration and force are vectors. Now let's talk about the mass in the equation. We think of mass as being a property of a particular section of matter, a particular object. And if you ask people about it, they'll often say, well mass is a measurement of how much matter I have. We have to be careful not to think about that how much as in how much space it takes up, because that's the volume. You can have a very fluffy object like a bunch of cotton balls that take up a lot of space, but don't have much mass. So if we really wanted to find what mass is, we come back to the concept of inertia. An object that's got more mass, well it's harder to change its motion. And an object with less mass, it's easier to change its motion. In terms of our equation, that means more mass, I need a larger force to get it moving. Smaller mass, I can get the same motion with a smaller force. Or if I apply a particular force to an object which has a very large mass, as mass is now on the bottom, I get a small acceleration. That same force applied to an object with very little mass, I'm going to get a larger acceleration. So mass ends up being related to force and acceleration by how much does it resist changing its motion. That's the introduction to Newton's second law, so you're going to get plenty of practice actually applying it.