Here is an area mechanics were going to talk about static equilibrium. That is, when you have an extended object, and by that, I just mean not a point mass, but an object that is not moving. So we're talking about really easy kinematics here. What does that mean? It's not moving, It's not accelerating. What does that mean? It was not accelerating then the sum of the forces must be 0. So no net external force. In addition to not translating with acceleration, it's does no angular acceleration. If it's static, it's not moving so, and no net external torque. So really, these problems are about finding what tensions in forces are created or do you need to hold this thing static like a bridge, right? If we want the bridge to actually work. So, a pretty standard first problem, and this is to have the case of wall and you've got a rod like holding a sign or something and the rod is attached to the building, right there. And, so it doesn't have to have a huge torque right here, ripping bricks out of the building. You've got a cable, something like that. So the cables attached to building, the cables under some tension, it's at an angle theta. And you may want to say, well, I have this at 30 degrees in this ways so much. How much attention does it cable have to withstand? That would be an important thing to know, and then you know what kind of material you have to use. Let's see, so if you want to look at this, let's define a coordinate system here. Let's make it at, my God, x in that direction, y in that direction, so z would be out of the board, x,y,z. And it feels like an embarrassment of riches here, because we have six equations. Right off the bat and any kinematics or any static equilibrium problem. Six equations to play with. You have the some of the external forces in the x = 0. They have the some of the external forces in the y = 0, you have the some of the external forces in the z = 0 and you have the sum of the external torques. And the around the x axis = 0, and you have the some of the external torques around the y axis = 0, and you have the some of the external torques around the z axis = 0. How could you possibly go wrong with that many equations? You could have six unknowns and still solve the problem. And you say, wait, I thought we had to pick one access? We'll remember you pick a point and you return the point, and typically you pick an access also. But really, you could think about once you say you're going to think about the access bar around this axis, you can say, well, that's z, but it could also rotate around y and x. So really, you have all three of those. But, that sounds exciting to have six, but in most problems, you use I'll say, three. because most problems are really thinking about the forces in a plane in the rotation around an axis perpendicular to that plane. That's what we usually limited to. So usually we're limited to 2 forces and 1 torque. I mean, not use the cross product sample 2, 4 and 1 torque, like that. In this case, the torques would be around the z axis and the forces would be all the x and y components of the forces. So this is how you set it up, so that one of the problems even about, right? So you have unknowns and a bunch of forces were usually doing? Usually finding F's tensions, right, and usually have to use are often have to think about at least the center of mass, For the center of gravity, in this case, they were kind of in the same position. And also you have to think about friction. These problems are often, About friction forces, and you have enough friction to keep the ladder from falling down, etc. So we're going to do a couple of these just to give you an idea of how they work
