>> Hello, class, let's talk a little bit more about torque. We had mentioned some ideas of torque in relation to the cross product, but there's another way to think about torque, which I think is very effective, and that's the following. It's equal to force times lever arm. Now this seems like a very simple concept. What becomes kind of challenging is to determine what we mean by lever arm. Force I think we understand force at this point, but what do we mean by lever arm? It turns out there's a very nice prescription for finding the lever arm. And what you do is the following. You extend the line of force, f, and then you find the shortest distance from that line of force to the axis of rotation. Some textbooks they call that line the line of action. Same idea, right. What direction are you pulling on it or pushing on it. All right. Let's see if we can do this with the problem that we had a little bit ago, which was opening the door. We said we're going to apply a force in that direction. And r is right there. That's the length of the door. If we want to calculate the torque in this case we can do our cross product thing that we had before or we could do this approach. Let's find the lever arm and then we'll calculate the torque based on that lever arm. So the prescription is the following. Step one, extend the line of force. All right. We'll just draw a dash line. That's our line of force. Find the shortest distance from that line of force to the axis of rotation. So we need to know a little bit about where our axis of rotation is. Well in our picture before that was the hinge, so that is clearly our axis of rotation. So now let me ask you guys, where should I draw that lever arm? Where is the shortest distance from that line to the axis of rotation? Mitchell, what do you think? >> (student speaking) Perpendicular to the force line. >> Perpendicular to the force line, okay. There we go. Right there, is that good? >> (student speaking) Yes. No, from the axis of rotation. >> Looks horrible, right? I drew it horrible on purpose. So Mitchell said perpendicular from the force line to the axis of rotation. That is of course the right answer. And it's right there. This is a perpendicular and this is what we're calling our lever arm. Okay. Any other line I draw anywhere. If I draw r. If I draw something up here. All of those are going to be longer than that line. All right. Shortest distance between two points is a straight line. Shortest distance from a line to the axis of rotation has to be perpendicular to that line. All right. So now we just have to identify what that lever arm is, and to do that we can go back to our earlier definition of this angle right here. That was phi. If that is phi then these two lines that are intersecting, that means that this angle is also phi. And now look, I have a right triangle here. I know the hypotenuse of the triangle. I know that angle phi I can write down what the lever arm is, because we know that the sine of phi is opposite, which is our lever arm divided by hypotenuse, which is r. And so the lever arm is just r sine phi. And now we can calculate the torque. Torque is equal to force times lever arm. The force is just f. It's just the magnitude f and the lever arm we just wrote down, r sine phi and this is exactly what we had before when we talked about the cross product. Okay. So remember this one. Torque is force times lever arm. It will carry you well into the future as you go work on your bicycle, if you work on your car. If you try to open the door to get out of the classroom, because the lecture is over. You can't wait to go get that next cup of coffee. All right. Questions about this? Christian, you have a question? >> (student speaking) Yeah. I was just wondering. So force is measured in what units? >> So let's take a look, right. Force we know is Newtons. >> (student speaking) Or Torque, I'm sorry, yeah. >> Okay. So we're going to have force times lever arm. So we don't know what that is yet, but we know that force is Newtons and lever arm is a distance, so that is meters. So apparently torque is Newton meter, and that's the SI units of torque. >> (student speaking) And then English is foot pounds, right? >> Right. So when you're working on your car and you buy a torque wrench it doesn't say Newton meters on it. >> (student speaking) Right. >> It says "foot pounds." Right. And that's the English equivalent of this, of course, and it says "How many feet, how many pounds do I apply to twist that bolt onto the engine?" And the way torque wrench works is there is a release that won't let you apply more than that torque, okay. If you apply too much torque you can snap the head off the bolt, you can strip the threads and so you want to apply up to that amount of torque. And what a torque wrench does is it has a little release that says, "Once I get to that amount torque I can't tighten anymore" and the torque wrench will click. Right. It's like a little clutch release mechanism in there. Okay. So foot pounds is a measure of torque. Yeah. Okay. Any other questions about this stuff before we move on? Everybody going to work on their car now?