Let's calculate a torque. To do it, let's think first, though, a little bit about it. It depends on the force, of course, the force creates the torque. But not only on the force, but also where it is applied relative to the rotation axis. So just like the moment doesn't just depend on the mass. It depends on how the mass is distributed. So the torque doesn't just depend on the force. It depends on where the force is pushing. So the formula is a vector formula. So torque is a vector, and we've got this r is a vector, and we're going to cross it with the force that's creating the torque. So t or tau is r cross f. So let's make sure we know what this all is. What these are, this is the torque. And now you can see its units are Newton meters. And people are always bothered that it has the same units as energy. It looks like a watch, right? A Newton up. Looks like a jewel. People are as bothered why this is the same units as energy. And I think there must be some deep meaning. Doesn't mean anything. It's meaningless. They just happen at the same unit. Get over it. Don't worry about it. r, this is the vector. This is the one you've got to get good at finding. Vector from the rotation axis to the point the force is applied. Not necessarily a radius. It's just a displacement from the axis to where the force is applied. And then this, of course, is just the force. And the force is a vector. So that's the three components. So we are going to first look at it by doing one thing, by opening a door. You apply a torque anytime you open a door. So let's look at it. Imagine we're going to open this nice door over here. And if you look down on the door, that looks like this. It's a big, long object like that. And it's got a hinge. So whenever something has a hinge, rotates on a hinge, that is where the rotation axis is. It doesn't rotate about its center of mass or anything. It rotates wherever the hinge is. That's what a hinge does. So it rotates on this end. And now the handle for a door. Is it ever on the side where the hinge is? No. It's on the other side. Because that makes it easier to apply a big torque. So what we're going to do is pull the door open. We're going to apply our force like that. There's our force vector. And now where is the R vector? Well, let's read. It's the vector from the rotation axis to the point the force is applied. We'll assume the door is thin. We won't worry about the fact that we're pulling from one edge of the door. We'll just draw it like that. So there's R right there. Now let's see. So now, let's see just apply our formula. Now let's see how the torque is R cross F. All right. So to get that part right, you've got to work on the magnitude and the direction. So let's do the magnitude. Right. The magnitude of the torque is for a cross product is the magnitude of the R vector, times the magnitude of the F vector, the distance, the force, and then the sign of the angle between them. But you've got to be very careful getting the angle between them. So if we're going to do this really proper with signs and everything, you've got to draw them tail to tail. So there are is that way. We're going to apply F that way. So it is a 90 degree angle. But then you've got to say it's R to F. So this direction, so is that positive 90 or negative 90? That's positive, because that's counterclockwise R to F. So in this case, it's a sign of 90 degrees, which is 1. So the magnitude in this case is just the radius of the door, the distance from the hinge to the handle, and how many newtons of force we have to apply. So we went in the demo closet, and we did that with that door. So as you can see, I pulled and to break the friction to get it moving, took about six newtons. And we measured the sort of distance from the hinge to about where the handle is, and that was 110 centimeters. So let's plug those in 1.1 meters times six newtons. So you can see then the torque in this case is 6.6 Newton meters. And the sign theta doesn't do anything, because we really did pull at right angles to the door. If you keep pulling, your angle might change. But the first, you pull perpendicular to the door's surface. At least we did in that case. You could ask yourself, now let's see. That's the magnitude of the torque, but torque is a vector. Just like all the other angular quantities, torque is a vector. It's a little hard to decide which way it points, but just like the angular quantities, it points perpendicular to the circular or the rotational motion. So we can get it from the right-hand rule, basically, R cross F. So remember the right-hand rule, you put your fingers along R, you curve them towards F. And in this case, we can see the torque vector is out. So we could draw a torque vector like that. Coming out of the board, there it is. Another way you can get the direction of the torque vector, if you don't want to do the cross product, is it has its own right-hand rule. You make your fingers curl along the direction the torque would like to produce force. And your thumb will be the direction of the torque vector. So it's own personal right-hand rule.