 So now we're going to look at the concept of static equilibrium. To do that, we're going to define a couple of words, static and equilibrium. Static means that it's not moving, and equilibrium means that everything's balanced. So I need a system that's not moving and everything is balanced. Now for rigid objects, all forces have to be balanced in all directions, and that includes the x direction, the y direction, and even though we don't talk about it too often, the z direction. I often think about x and y is right and left, y is up and down, and z is kind of like the back and the forth towards your away from you. Also for rigid objects, all torques have to be balanced at all pivot points. When we start solving problems, you'll see how this can be very helpful, but in terms of an equation, it's the sum of the torques has to be equal to zero. Now in terms of a general strategy, the first thing you have to do when you approach a static equilibrium problem is to identify all forces with their locations. If you accidentally leave some forces out, you could end up getting the wrong answer, and this is the same as when we had force diagrams back in motion in two dimensions. Don't forget your pivot point forces. Sometimes there are forces holding a particular pivot point as a fixed point, and there's got to be forces to do that, even though we may not think of them as being applied forces at that point. After you know all your forces, then we construct our force equations. Then we construct our torque equation. You have to do some algebra, plug in your numbers to do the math, and as always, check your answer when you're done. Now I'm going to show you an example here of just part of that, using a balanced scale. So here you've got something which is balanced here on a pivot point. And I might have some sort of long rod in the middle that's sitting on some sort of frictionless pivot point. Now if I put a mass over here on one side, it would tend to make the board want to tip down on that side. But if I put another mass on the other side, it could balance out so that it stays balanced. We're going to use this as our example. So let's think about the forces on this. Obviously there's a force due to the mass pushing down over here on one side, and a force due to the mass pushing down over here on this side. Now those aren't the only forces. There's a pivot point, and at that pivot point, there's the force of the pivot holding the board up. Now also what we don't want to forget is the board itself probably has a mass. And if we think of our center of gravity concept, we're going to have that right there at the center. Now once you've drawn in your forces at the location, or even as you're drawing in your forces, you want to go ahead and label them with as much information as you can. For example, my first mass, well the force is the force of gravity, so that's going to be M1g. And I'd have M2g for my second mass. And I could label a little mb for the mass of the board, g here. And then that pivot point, well I'm sitting on top of that pivot, so I could call it a normal force. Even if you were to label these just as F1, F2, F3, make sure that your diagram shows your force labels so you can start to construct your equations. Now the first equation I have to work with, it's going to be an easy one. Some of the forces in X, there are none. So although this is a perfectly correct equation, it doesn't really give me any information to solve anything. Similarly, for this problem, and most of the 2D type problems you're going to be solving, there's nothing in the Z direction either. But the Y, now the Y direction is going to be interesting. There's lots of forces in the Y direction, and when I construct my force equation I have to take into account their direction. So of all these forces, the one in the positive Y direction is the normal force. So that goes in there as a positive. The other three forces, m1, g, m2, g, mb, g are all in the negative direction. In Y, negative is downwards. And that has to add up to be zero. So this is one equation that we could use as we start to solve this particular problem. Now for the torques. Now for the torque equations, you need to still have all your forces labeled and where they're at, but you have to do a little bit of extra steps. In particular, you want to figure out a pivot point to use. And in this one, it makes sense to put my pivot point right here at the center. The next step is to actually figure out our distances. So if I want m1, I need to recognize that it's at a distance and I can call it r1 from the pivot point. And that might be given or it might be something I have to find. Similarly, mass two is out at a distance r2 from the pivot point. And these r's don't care if they're positive or negatives at this point. I just need to know how far is the force from the pivot point. Now when it comes to the normal force and the weight of the board, I don't have to specify my distance because they're at the pivot point. They have a distance of zero. And so that means in terms of the torques, they're not going to come into the equation. So when I start creating it, I also have to determine the directions. You see, mass one is going to tend to tilt the board in this direction. And that is the counter-clockwise direction. So that's a positive torque if we're using our standard definitions. Mass two, though, is going to tend to make it tilt in this direction, which is the clockwise direction. And we're using that as a negative. So when I go to create my sum of the torques, I only include the forces which are at a distance from the pivot point. And I have to include the plus or minus signs for each of those terms. And those have to balance out to be zero. So in this case, I had one force equation, the sum of the forces and y, and one torque equation that I can use. Now for this particular problem, I haven't given you any numbers or asked you any particular thing to solve. But that would be the next step to go through is to actually plug in the things you know and solve for the things you don't know. So that's an introduction to static equilibrium. We'll look at some more examples and work through the whole process of doing the algebra later.