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## Net Torque & Sign of Torque

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Hey, guys. So in this video, we're gonna talk about what happens when you have multiple forces producing multiple torques on the same object. In other words, trying to get the object to spend in different directions. Let's check it out. So the first thing we need to talk about is the sign of torque. Okay. You might remember that with different forces. Um, if you have a force going in different directions like the positive exacts the native X axis, we use signs to indicate direction. Same thing happens with torques, but the direction depends on which way you're trying to spin something. All right, So if you're trying to spend something in the clockwise direction, which is direction of the clock, it's negative, and counter clockwise is positive. Now there's two ways that you can remember this. The reason counterclockwise positive is because it follows the unit circle, right? The unit circle spins this way. It starts at zero degrees over here, and he grows in that direction another way you can think about this. Is that the clock? The direction of the clock, um is backwards Clock is backwards. Okay, Those are two ways that you can remember the direction This is a standard direction for rotation eso. You should remember that now. What happens if you have multiple torques? You have multiple torques. We can calculate the net torque. The network is the result of torque. It's one torque that represents a combination of all of them. Okay, and the network is simply the addition of the individual torques. So if you have to torques, it would look like simply talk one plus torque to now. The big difference between forces and torques is that forces are vectors. They have a direction of data that can be pointing in different directions. A torque is the result of a force, and a torque is a twist that's either clockwise or counterclockwise. That's not really a direction in the same way that a force can point of an infinite number of angles. This is just really two options. It's either going to the right or going to the left or just going clockwise or going counterclockwise. It's not a direction, um, in terms of data, so there is no data because they are scale. Er's not vectors. Um, they just haven't orientation that could be either positive or negative. Okay, so we're gonna use simple additions and not vector additions to find torque. Remember, for forces. If you push this way with the three in this way with a four, the Net force is not seven. The Net force is five. Because this is Vector Edition with torques. If you have a torque of three and a torque of four, the answer is always seven because it's simple Edition, not vector Edition forces are vectors, torques or scaler. Let's do a quick example here. So have to forces acting the same door. The door is 3 m long. Um says forced one acts in the center of the door. So this is the middle right here. So I'm gonna say that this is 1.5 half of the length and this is 15 the other half of the length. It's as if to is directed at 30 degrees above the X axis. So it looks like this, and we want to know what is the net torque. And we also want to use, um, signs positive or negative to indicate whether the clockwise or counterclockwise, the direction, the orientation of the torques. Okay, the direction of the spin, I should say. All right, Um So what we're gonna do is we're gonna do torque one plus torque to There are two torture to force is therefore, there could be as many as two torques. I want to remind you that a force may give you a torque. So if you have two forces, you could have two torques. You could have one. You could have zero, but you can't have three. Okay, so the maximum amount of torque so you can have is the number of forces you have to go into that I'm gonna right. I'm gonna expand each one of these guys. The definition of torque is f r sine of data, so it's gonna be f one are one sign of data one. I'm gonna leave a little space here for us to indicate whether that torque is positive or negative, and I'm gonna do the same thing here. F two R two sign of data to now Remember to solve torque problems. There's three steps are you have to draw your are vector. You have to figure out your data and then finally you plug it into the torque equation. So let's do that first. Let's right the RV. Let's draw the our vector for each one of these guys. What's our one and what What are too are is a vector, an arrow from the axis of rotation to the point where the force is applied. So our one is from the axis over here to the point where the force is applied. R one R two is from here, all the way to the end. This is are two over. Here are one is 15 and R two is three. Um, meters. So we got those two guys figured out. Now, how do we know which way it moves? We're going to use the our vector to figure out whether they are, whether these individual torques or positive or negative. Okay. And I want you to think of Here's the door, which is my our vector is happening along the door. And I want you to think of what would happen if you pull on the door or on your arm in these directions. So f one is pointing down this way right here at one. Pointing down. Okay, So what you have imagine if you're pulling on your arm like this. Right? But I can pull my thumb down like this. Um, this would spin in this direction. Okay, This would spin this direction so I can say that F one eyes trying to get this thing to have a torque in this direction. I'm gonna call this Torque one. Okay, Now, let's put the bar back here. The door. What If you're pulling this way, F two, then you can think about it this way or just pull a finger in angle, right? If you pull it this way, it's gonna try to cause it to spin like this, right? Even though it's not 90 degrees, it's at an angle. It's still gonna cause it's still gonna try to do it this way. And that's because it's basically, um if you are above this line here, you're gonna do that. And if you are any tiny bit below this line, you're gonna cause it to do this way. You're gonna cause rotation to go that way. So what you do is you extend your are vector, and if you are on top of it, you're gonna go like that If you're if you're pulling sort of below it. You're gonna go like this. Okay, So torque to is in this direction. Now what signs air these. Well, this is going in a clockwise direction. T one So T ones negative and t two is going in a counter clockwise in the direction of unit circle, so it is going to be positive. OK, so this guy is negative. This guy's positive. Let's put those signs here. Torque one is negative. Torque to is positive. The rest is what we've been doing so far, which is plugging in these numbers. So negative. The forces air both 50. The distance for our one right here. 1.5 sign of data. The angle between r one R one is the blue line and this one. So our one and F one, the angle here is 90 degrees easy. This guy is positive. So 50 or choose the entire length of the door. So it's three. Okay, in sign of now, I have to make sure this is the correct angle. So let's be careful here. I'm going to redraw our I'm going to redraw f. Okay. Remember one of the things you can do You want them to be either all joining at the same point or or exiting the same point. You basically wanna make this easier for you to see, Um, s Oh, there's a few ways you could do this. I think the easiest one is just to move this our director up like this on. And then you can see that this is, in fact, the angle you want, which is the angle that's given. So in this case, the angle given to you was the angle you're supposed to use. But remember, a lot of the times you're not supposed to use, uh, the angle you're given is not the one you're supposed to use. Okay, so I have to be careful here. Just worked out that way. So that's nice. Sign of 90 is one and sign of 30 is points five. Okay, so this is going to be negative. 75. Um, negative. 75 plus 75. So this is interesting. They both added up to zero. What does that mean? Well, if they both added up to zero, it means that they perfectly cancel each other out. And you actually have no rotation at all. So the network here the sum of all torques, which is the same thing as net torque is zero. And what that means we'll talk more about that later is that you have rotational equilibrium. The two forces there, the two torques are canceling, so the object actually doesn't spend it all. We'll talk about that a little bit later, but that's it for this one. Cool, Let me know if you have any questions and let's keep going.

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Problem

A 2-m long bar is free to rotate about an axis located 0.7 m from one of its ends. Two forces act on the bar, F_{1} = 100 N and F_{2} = 200 N, and both make 30° with the bar. Find the Net Torque on the bar. Use +/− to indicate direction.

A

−95 N•m

B

+95 N•m

C

−165 N•m

D

+165 N•m

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