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# Moments

## Video transcript

welcome to the presentation on moments so just if you were wondering I have already covered moments you just may not have recognized it because I covered it in mechanical advantage in torque but I do realize that when I covered it in mechanical advantage in torque I think I may be over complicated it and if anything I didn't cover some of the most basic moment of force problems that you see in in your standard physics class especially physics classes that aren't you know focused on calculus or you know I'm going to make you a mechanical engineer at the very next year so we we did that with what I write down the word mechanical oh yeah mechanical advantage that's if you do a search for a mechanical advantage I have I cover some some things on moments and also on torque so what is moment of force well it essentially is the same thing as torque it's just another word for it and it's essentially force times the distance to your axis of rotation what do I mean by that let me take a simple example let's say that I have a pivot point here let's say I'm a pivot point here let's say I have some type of some type of seesaw or whatever there's a seesaw and let's say that I were to apply some force here and the forces the forces that we care about and this was the exact same case with torque because they're essentially the same thing the forces we care about are the forces that are perpendicular to the distance from our axis of rotation right so in this case if we're here the distance from our axis of rotation is this that's our distance from axis of rotation so we care about a perpendicular force either a force going up like that or force going down like that so let's say I have a force going up like that let's call that F f1 d1 so essentially the moment of force created by this force is equal to f1 times d1 or the perpendicular force times the moment arm distance this is the moment arm distance moment moment arm that's also often called the lever arm if you're talking about a simple machine and I think that's what the term I use when I when I did a video on torque moment arm and why is this interesting well first of all this force times distance or this moment of force or this torque if it has nothing balancing it or no offsetting moment or torque it's going to cause this this seesaw in this example to rotate clockwise right this whole thing since it's pivoting here is going to rotate clockwise the only way that it's not going to rotate clockwise is if I have something keep so right now you know this descent is going to want to go down like that and the only way that that I can keep it from happening is if I exert some upward force here so let's say that I exert some upward force here that perfectly counter balances that keeps that keeps this whole seesaw from rotating f2 and it is a distance d2 away from our axis of rotation but it's going in a counterclockwise direction so it wants to go like that so the law of moments essentially tells us and we learned this when we talked about the net torque essentially tells us that this force times this distance is equal to this force times this distance so f1 d1 is equal to f2 d2 or if you subtract this from both sides you could get f2 d2 minus f1 d1 is equal to zero and actually this is how we dealt with it when we talked about torque because just the convention with torque is if we have a a counterclockwise rotation it's positive and this is a counterclockwise rotation and the example that I've drawn here and if we have a clockwise rotation it's it's an as a negative torque and that's just the convention we did and that's because torque is a pseudo vector but I don't want to confuse you right now what you'll see is that these moment problems are actually quiet quite straightforward so let's do a couple it always becomes a lot easier when you do a problem except when you try to erase things with green so let's say that let me let me plug in real numbers for these values here let me erase all of this let me erase some of my let me just erase everything there you go all right let me draw a lever arm again so what we learned when we learned about torque is that an object won't rotate if the net torque the sum of all of the torques around it or zero and we're going to apply essentially that same principle here so I said if I have let's say let's do it with masses because I think that that helps explain a lot of things and makes the seesaw example a little bit more tangible let's say let's say I have a five kilogram mass here five kilogram and let's just say that that gravity is 10 meters per second squared right so what is the downward force here what is the downward force it's going to be the mass times acceleration so it's going to be 50 Newtons and let's say that the distance the moment arm distance or the lever arm distance here and all let's say that this this distance right here is 10 meters and let's say that I have another mass I don't know let's say it's a let's say it's a 25 kilogram now that's too much let's say it's 10 kilograms let's say I have a 10 kilogram mass 10 kilogram mass and I want to place it some distance D from from the fulcrum or from the axis of rotation so that it completely balances this 5 kilogram mass so how far from the axis of rotation do I put this 10 tilaka 10 kilogram mass this is the distance right because we actually care the center of the mass well how much force is this 10 kilogram mass exerting downwards well as 10 kilograms times 10 meters per second squared it's a hundred Newton's so and then there this is acting what this is acting clockwise all right this one's acting clockwise and this one's acting counterclockwise all right so they are offsetting each other so we could do it a couple of ways we could say that 50 Newtons the moment in the in the counterclockwise direction 50 Newton's times 10 meters in order for this thing to not rotate has to be equal to the moment in the clockwise direction and so the moment in the clockwise direction is equal to 100 Newton's 100 Newton's times some distance some distance let's call that D 100 times D and then we could just solve for D right we get 50 times 10 is five hundred five hundred Newton meters is equal to 100 Newton's times D that's 100 divide both sides by 100 you get five meters is equal to D so D is equal to five and that's interesting and I think this kind of confirms your intuition from playing at the playground that you can put a heavier weight closer to the axis of rotation to offset a light weight that's further away or the other way to put it is you could put a light weight further away and you kind of get a mechanical advantage in terms of offsetting the heavier weight so let's do a let's do a a more a more difficult problem I think the more problems we do here the more sense everything will make so let's say let me let me let's say that we have a bunch of masses let's say that we have a bunch of masses actually let's not do it with masses let's just do it with forces because I want to complicate the issue so this is the pivot and let's say I have a force here that's 10 Newtons going in the clockwise direction and let's say it is it is that let's say if this is zero let's say that this is at minus 8 so this distance is 8 all right let's say that I have another force going down at 5 Newtons and let's say that its x-coordinate is I don't know minus six let's say I have another force that's going up here and let's say that it is 50 Newtons this might get complicated 50 Newtons and it's at minus two so it's this distance right here is two right now let's say that I need to figure out let's say that I have a not making this up on the fly let's say that I'm have another force here that is 5 Newton let's make it a weird number 6 Newtons and this is this distance right here is 3 meters and let's say that I need to figure out what force I need to apply here upwards or downwards I actually don't know because I'm doing this on the fly to make sure that this whole thing doesn't rotate right so to make sure this whole thing doesn't rotate essentially what we have to say is is that all of the counterclockwise forces all of the counterclockwise moments or all of the counterclockwise torques have to offset all of the clockwise torques so what are all and then notice they're not all on the same side so what are all of the things that are acting in the counterclockwise direction so counter clockwise is that way right so this is acting counterclockwise this is acting counterclockwise and that's it right and so the other ones are clockwise and we don't know this one let's assume let's assume for a second well let's assume we could assume either way and if we get a negative that means it's the opposite so let's assume that this is a that bit and so let me all of the clockwise ones all doing this dark brown so this is clockwise let's assume that this is clockwise and let's assume that our mystery force is also clockwise right so all the clockwise moments have to offset all of the counterclockwise moments have to offset all of the clockwise moments so what are the clock what are the counterclockwise moments well this one's counterclockwise so it's 10 Newton's 10 times its distance from its moment arm we said it's 8 right because it's the x-coordinate minus 8 from 0 so it's 10 times 8 plus 50 right this is also counterclockwise times 6 50 times 6 and that was all those are all of our counterclockwise moments and that has to equal the clockwise moment so clockwise moments let's see we have five Newton's that is going clockwise times six five Newton's actually was this was the six know if this is six I must have written some other number here that I can't read now how far did I say this was I know let's say that this is two so that 50 is let's say that this is two it's negative two because that's what it looks like I apologize for confusing you so what we're all the clock counterclockwise moments this 10 Newton times its distance 8 the 50 Newton's times this distance - and don't get fused by the negative I just kind of said we're in the x coordinate axis or minus 8 if this is zero but it's 8 units away right and this 50 it's it's moment arm distance is 2 units and so that has to equal all of the clockwise all of the clockwise moments so the clockwise moments is 5 Newton's times 6 right its distance is 6 and it's 5 Newton's going in the clockwise direction and then we have plus 6 Newton's times 3 plus 6 times 3 and then we're just assuming we don't know for sure our force our force and let's say we're applying the force I should have told you ahead of time so you can do this problem let's say that we're applying the force set at 10 units 10 meters away from our fulcrum arm so force times 10 so now let's just solve for the force we get 80 plus 100 is equal to 30 plus 18 plus 10 F we get 180 is equal to 48 plus 10 F what's 180 minus 48 it's 32 132 so we get 132 is equal to 10 F or we get F is equal to thirteen point two Newtons so if we apply so we guessed correctly that this is going to be a clockwise sorry this is going to be a I when I keep mixing mixing up all over clockwise and counter-clockwise Latia that this this is going to be a clockwise force right these were all of the this is going to be a counterclockwise voice right o'clock this is counterclockwise so all of these let me label that because I think I said it wrong several times in the video so these are the these go clockwise clockwise and it's this one and this one and what were the counterclockwise these go counterclockwise so we have to apply a 13-point 10 Newton force 10 metres away which will generate 132 Newton metres moment in the counterclockwise direction which will perfectly offset all of the other moments and our lever will not move anyway I might have confused you with all the counterclockwise clockwise but just keep in mind that all the moments in one rotational direction have to offset all the moments in the other rotational direction and all a moment is is the force times the distance from the fulcrum so Force Times distance fulcrum arm force times distance forearm I'll see you in the next video