Hey guys. So in this video, we're going to introduce the idea of torque, which is the rotational equivalent of force. Let's check it out. Alright. So you can think of torque as a twist that a force gives an object around an axis of rotation. Here's the most classic example. If you have a door that is fixed around an axis here, this is the hinge of the door which is also its axis of rotation, meaning the door is free to rotate around the axis. And if you push this way with a force f, it causes the door to spin this way. I'm going to say that the door accelerates in that direction. It gains an alpha. So when you push on a door, it rotates around its hinges. More generally speaking, when a force acts on an object as it does here, away from its axis, it produces a torque on it. Let's talk about these two parts, away from the axis. If you push on a door here, it doesn't actually cause spinning. I'm going to say alpha equals 0. Right? If you try to open the door by pushing the hinge, it doesn't spin. You have to be away from the axis of rotation. And then it produces a torque. So this is the idea that a force causes a torque which causes an acceleration. So what you're doing, you're not producing a torque, you're producing a force which then results in a torque on that object. So now the other point is that a force may produce a torque. We already talked about how if you push here, it doesn't cause it to rotate so you don't produce a torque. So force may or may not produce a torque and a torque may or may not produce a rotation, an angular acceleration. And that's, let's say if you're pushing this way, but then someone else, F2 is pushing this way and these 2 cancel out. In that case, it wouldn't really produce them. But the most important point I want to make is that you have f produces a t, which produces an alpha. That's the sequence. We just talked about this. Let's fill it in here. Similar to forces cause linear acceleration, remember, sum of all forces equals m a. Sum of all forces, as long as you have a net force, you're going to have an acceleration. It's the same thing with torques. Torques cause angular acceleration. We're not going to talk about that just yet, alpha. We're going to talk about this a little bit later. Now another difference between torque and force is that force is a straightforward number. If I tell you we push with 10, that's the end of it. But for torques, torque depends on how hard you push, it depends on how far you push, and some other stuff. So, we actually have an equation for torque. You don't have an equation for force. You're given a force, but for torque, you have to calculate it. And it is frsin⁡⁡⁡θ, where f is the force you push with, it's a vector. R is a vector. It says here r is a vector from the axis of rotation to the point where the force is applied. Remember, little r in most rotation problems has to do with distance from the center. It's the same thing here. Now theta is the angle between these two vectors. See these two vectors right here, f and r? Theta is simply the angle between those two guys. f and r are meant to put an f and an r. And one thing I like to do is I like to think of like an arrow pointing towards these two guys here. Right? And that's to remind me that in that equation, the theta is the angle between the f and the r. The 2 guys are hanging out next to the theta. Okay? Theta is the angle between these two guys. Now the unit for force is newtons. The newton for the units for distance r is meters. So torque is measured in newton times meter. Okay? That's the units for torque. One last point that I want to make here is that when we need to maximize the torque, to get the most possible torque, another way to think about this is the way to apply the least amount of force and get the most amount of results to be the most efficient with causing something to rotate is to apply the force as far as possible and perpendicular and apply the force perpendicular, perpendicular to the r vector. Perpendicular means 90 degrees. It's got the little perpendicular symbol, to the r vector. So what does that mean? So let's draw the r vector real quick on this picture here. The r vector is from the axis of the rotation, which is here, to the point where the force is applied, which is over here. This is the r vector. You want your force to make this is your force. You want your force to make 90 degrees with the vector, which in this case, it does. That's how you get the maximum torque, the easiest way to rotate. Imagine if you're instead pushing the door this way, right? This would be a little bit weaker. You have to push harder to get the same rotation. So you want to push at an angle of 90 degrees. The other thing is that you want to push as far as possible away from the axis of rotation. So you've all opened doors before. If you try to open the door by pushing on it, let's say right here, I'm going to make a little bit of a mess, but I'm going to erase this. If you push right here, it's much harder to open the door here than to open the door at the end. In fact, that's why the doorknob is on the opposite side of the hinge because that's where you're supposed to push. It's easiest. So, and you can relate that directly to the equation, right? So if you want the torque to be as high as possible, you obviously want to push as much as hard as you can, as far away or as distance from the axis, as far away as you can. And you want to maximize sine of theta. Now let me remind you that sine and cosine fluctuate between negative one and one. Right? So it looks like that. So the greatest possible value of sine you can have is 1. Now where does this happen? This happens when theta is 0 I'm sorry, when theta is 90. Sine of 90 is 1. That's why if you look at the equation, that's why you get the greatest possible value for torque. Okay? So again, your torque is maxed when you push as far away from the edge as possible and when you push perpendicular, make it a 90 degree angle with the r vector. Alright? Now let's do an exam