Net Torque on a disc

by Patrick Ford
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Hey, guys. So in this way I want to show you how to calculate torque on a disk with forces in a bunch of different directions. Now, this picture looks sort of scary at first. What's what's going on with all these arrows on? You may not see something as complicated as this. I'm putting it all together so we can talk about it all at once. But you should know how to handle all these different situations, individually or together. Let's check it out. Eso Here we have a composite disc, which means there's two different discs. You got the inner disc, which is the dark one here and then the outer disc. Your this is so you can have two different radio. Um, they are free to rotate about a fixed axis perpendicular through its center. So basically, the disk skin spin this way, right? All the forces listed here are 100 Newtons, and there's four of them, So let's just write F one actually make this one half one half one f two F three and this one's gonna have four. They're all 100 on the angles are 37. The only angle here is 37 is this one. All the other ones are sort of either flattened the X or flattened. Why the dotted lines are either exactly parallel or exactly perpendicular to each other. What does that mean? That just means that this line is the same is this line They're parallel to each other and that these lines here make a 90 degree angle. So all these lines were making 90 degree angles with each other Cope Thea inner disk has a radius of 3 m. What? That means that this distance here is 3 m and an outer radius of on the outer disk has a radius of 5 m. Which means that this line over here, this entire distance over here is 5 m. Okay, We wanna know that net torque produced on disk about its central axes. Um, we're gonna use plus reminders to indicate direction clockwise clockwise. So the net torque torque net is the same thing as the sum of all torques. There are four forces, so there's potentially four torques. Remember, a force may cause a torque. There are four forces, so you could have as many as four torques. But some forces may not cause of torque. So let's let's do one by one. Here, Torque one. This guy is F one. Let's first, actually, the space for the sign. Positive. Negative. So we don't forget. Um, f one r one sign of data one, and we'll do the sign a little later. The first thing we do I know if second plug that in there, it's pretty straightforward. First thing we do is we draw on our vector. Then we figure out data and then we figure out the sign. Okay, So the our vector, um, is the distance is the vector from the axis of rotation to the point where the force happens In this case, the our vector for F one is a narrow this way. This is our one and are one has a length of the outer disc, which is five. Okay. And then sign of feta. The angle that are one makes that F one is 90 degrees. So I'm gonna put a 90 here now in terms of sign, imagine you have a disk and you're pushing this way on the disk. So you have a disk and you're pulling like this. So the disk is going like this because you're pulling this direction, right? You can also imagine, as you're, like, sort of stroking the disk this way, right? This is gonna spend like that. Um, so this is going to be a positive torque, because it's causing this to spend in a counter clockwise in the direction of the unit circle. So it's positive this is one and you just end up with positive of torque. 500 Newton meter. All right, so talk to box F two R to sign of data to I know f choose 100 but I gotta figure out our and feta so I'll leave those blank. Um, f two is right here. F two acts in the middle of the acts on top of the axis of rotation. Therefore, the R two will be zero r two equals zero, which means there is no torque at all. When you have something that pulls on the axis of rotation, it produces no Tory because there is no are. And you can see from the equation that the whole thing becomes hero. So it doesn't matter what the angle is, and it doesn't matter. What sign is because you just have zero. Okay, for torque. Three again. Box space for positive. Negative F three R three sign of data three and the forces 100. We gotta figure out our and Fada if you look at F three F three acts on the edge of the outer disk, this is what the R three vector looks like. Alright, Are three right here. So our three vector has a length of the outer radius, which is five. But the problem is thes two arrows, Macon angle of 180 degrees with each other. And the sign of 1 80 is zero. Okay, Sign of 1 80 is zero. So it doesn't matter what the sign is because, um whether it's positive or negative direction, because the torque will be zero. Imagine the disk. And if you push directly towards the middle of the disk, you don't cause the disks. It's spin. The only way to cause this to spin is to either push sort of tangentially on the disk or to, like, push it inning. Right. If you have a disk and you go like this, it's going to spin. But if you push like this on a disk. It doesn't spin. Okay, now let's do Torque four. This is the ugly one up here, and let's figure out what happened. So box. Um, I'm just gonna jump straight into it. The the F four is 100 radius sign of fade up. So this one, we're gonna slow down a little bit to be a little more careful. Notice that it's touching on the inner radius, Theo, inner disk. So I'm just going to redraw just the inner disc coming right here that this is a radius of three. Because it's the inner one. Let me make this a little bigger. Radius equals three. This force acts like this right there. This is the center. First thing we draw is the access. Um, the our vector. The our vector is from the access to the point where the force happens. Um, notice that here, this would look like this. So this dotted line is just an extension of your are vector. And there's an angle of 37 degrees here. Okay, so you got to figure out which angle to use. First of all, the distance will be the entire radius of the inner circle of the inner, um, disk. So it's three. And what about the vector? So what? You were not the angle. So what you could do is you get the art vector here, and you can extend it this way, right? And to make it easier to notice that this is, in fact, the angle, you should use its the angle between the two lines. So 37 is the correct angle. Okay. Remember, the angle given to you isn't always the one you're supposed to use. In fact, that's usually not the one you're supposed to use. Uh, but in this case, it turned out to be that way. What about the direction which this thing will spin? So you should imagine that if you're pushing a disk like this, it's actually gonna spin like this. One way that would make this easier is to think of this as a not as a, uh, not as a push on the disk, but as a pool. You're essentially pull into this. I'm sort of redrawing this f for over here, just kind of extending it down. You're pulling your pushing this way. You're causing it to go like that. Okay, um, so Hopefully, that makes sense. It's pretty. It's pretty visual thing there. But hopefully you can follow. That s o. This direction here is in the direction of the unit. Circle its counterclockwise. So it's positive. Okay, Positive. And if you multiply this whole thing, you get the torque. Four is positive. 1 80 Newton meter. And to find the network, we just add everything up. I got two of them that were zero. So it's just the positive 500 the positive 80 Which gives you positive. 6. 80 Newton meter. Okay, that's it for this one. Hopefully makes sense. Let me know if you have any questions and let's keep going.