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Anderson Video - Torque is a Vector

Professor Anderson
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 >> Hello class, Professor Anderson here. We're continuing our discussion about torque and what I wanted to say today is that torque is in fact a vector. It has a particular direction associated with it. And what we said last time was that direction is governed by the right hand rule, okay? But let's say we don't want to think in the third dimension, we just want to think in two dimensions. And I have a door that is going to be opened in this direction, that is, of course, a counterclockwise direction. And if the door opens the other way, that is, of course, the clockwise direction. Now typically, what we say is torque, tau, is positive if it is rotating counterclockwise. Torque, tau, is negative if it is rotating clockwise, okay? In three dimensions, we know that torque is into or out of the board. And once you draw a Cartesian coordinate system, you'll see that if I have X crossing with Y, I get Z, all right? So, that's how it's going to relate to the third dimensions -- to the third dimension. But just thinking in two dimensions, this is a perfectly adequate way to think about it. So, let's say we have two people trying to open the door. [ Background noise ] So, here's our door and you push on the end of the door with a force F but somebody else is trying to come in and they are pushing on the middle of the door with the same force, F. Let's see if, based on this sign convention, we can figure out who's going to win. This is, of course, our axis of rotation, where the hinges. And let's say that this length here is L over 2 and the whole length of the door is L. All right, we need to sum up the torques and torque is a vector, and so we have to take into account the direction. And the one that is trying to rotate the door counterclockwise is going to be the positive torque. So, which one is trying to rotate it counterclockwise? It's this one, right? If the other force isn't there and this one is the only one, it's going to go like that and that is our positive quantity. If these are right angles, then the lever arm is just the full length of the door, L What about the other guy? The other guy is trying to rotate it clockwise and so we put a negative sign in front of it. Its lever arm is halfway down the length of the door, and so it's L over 2. And now we see what happens, we get 1FL minus 1/2FL and so we end up with 1/2F times L. This is a positive number and so the door is going to rotate counterclockwise. This person wins. They are able to get out of the door. The other person clearly gets pushed out of the way, okay?