whenever you turn something you need a force and of course you need a pivot involved as well but of course if you push with the same Force further away from the pivot then you're able to turn the thing more easily so we need something to describe this physically this is where moments come in a moment is literally just the force that you apply to something times the distance that forces away from the pivot however there is a little bit of a caveat with this one we need to add in distance brackets from pivot perpendicular to the forces line of action let's just think of units for one second of course force is measured in Newtons distance is measured in meters so of course adding those up just putting those together we just have moments are measured in Newton M moment is also known as turning Force it's also known as T so for instance if I have a seesaw here here's my Pivot here's a mass on this end and its force is acting downwards obviously and let's say its weight is 20 newtons obv see we have to deal with the force not just its mass its distance from the pivot is 2 m therefore put simply the moment is equals to the force which is 20 time distance just going to be 2 * 20 that gives us 40 new M however if I had a 40 Newton weight I want this seesaw to balance where would I have to put that well you probably realize that I have to put it halfway between the pivot and the end of the plaque assuming that it's the same length either side so that means that this distance here is going to be 1 M what is the moment of this for 40 Newton weight well it's 40 * 1 and therefore that equals 40 nton m as well you probably realized that this is now going to be balanced it's not going to turn so that means it's in equilibrium in order for something to be in equilibrium there needs to be no resultant Force so that means it's not moving up down left right whatever and also that means it's not turning due to a force either now the principle of moments is for an object to be in equilibrium the sum of the anticlockwise moments have to equals the sum of the clockwise moments now of course looking at this weight here if it wasn't for this weight here which way would this weight pull the beam well of course the beam would go downwards so that's anticlockwise around the pivot what about this one here if it wasn't for this weight this weight would cause a moment that would pull the beam clockwise in order to balance we need this moment to equals this moment and of course if you have other moments involved on this side then you need same sum of moment moments on this side as well so the first thing you need to do is realize when you have a moment which direction is it pulling is it pulling clockwise or anticlockwise that's nice and easy when you have a system which actually has a nice pivot that's nice and obvious but what about if we have a lighting rig here I have a lighting rig say above a theater stage it's held up by two cables and those cables are supporting the weight of the light that's hanging off the beam and also the weight of the beam itself now sometimes you'll get given a question which will expect you to take into account the weight of the beam and sometimes you won't 99% of the time the weight for an object like a beam is going to be right in the center now I can tell you the weight of the light is 200 Newtons the weight of the beam is 80 Newtons now this time there's no obvious pivot but the system is still in equilibrium so the same must be true as it was earlier the sum of the clockwise moments have to equals the sum of the anticlockwise moments the question is is where is our pivot where do we say our distances are from what's weird is that it doesn't matter where you take moments about you can call for now any point on this system a pivot and it will still work as a rule of thumb when we're trying to find out two unknowns the first thing we want to do is make one of them the pivot itself so we're literally removing this one from the equation so if this is our pivot and these are our distances here then we can fairly easily find out what the forces of the tension in the cables is going to be so what we need to do is create our own equation using the idea that the sum of the anticlockwise moments equals the sum of the clockwise moments so using this as our pivot which way is the lamp pulling well that's obviously going to be clockwise the weight of the beam that's obviously clockwise as well the only one going anticlockwise is the tension in the cable so we therefore know that the moments due to this and this added up are going to be equals to the moment due to the tension so let's have a go at that then so we're going to say 0.5 * 200 that's the moment due to the light plus 1 * 80 that's our moment due to the beam it's going to be equals to the tension T2 times well our distance is two it's going to be equals to 2 T2 all we have to do then is rearrange that to find the answer you can have a go with that now if you want to hopefully you've got the tension in T2 as 90 Newtons so what about if we wanted to find out what the tension of T1 is well we could use T2 as our pivot now because then we'd have the moment due to this and this added up equals the moment due to T1 we could but there is an easier way because we know the two conditions for equilibrium are that the sum of the clockwise moments equals the sum of the anticlockwise moments but also there's no resultant force in other words all the downwards forces equals all the upwards forces so we can take a shortcut if you've only got one more Force involved then you don't have to take moments which is kind of nifty so we know that T2 plus T1 so that's T1 + 90 is going to be equals to 200 + 80 that's just saying that the upwards forces equals the downwards forces nothing to do with moments now because we've only got one force left to find out that gives us a tension of90 Newtons so providing that you remember the two conditions needed for an object to be in equilibrium you can work all of this out yourself as with a whole load of things in mechanics getting good at these requires practice so find some questions so far we've only seen situations where the forces are opposite to each other so up and down and left to right Etc but what if they're at different angles let's say we have a wall here and we have a shelf and we have a piece of wire keeping up this shelf let's say that we have a bunch of flowers hang in a little hanging basket here delightful that are pulling down with a weight W1 and I'm going to call the length of this beam L the only thing that's keeping this up is this piece of string that's halfway across the beam attached to it there I'm going to call that t CU it's got a tension but it's pulling up at an angle now that's a bit of a problem because of course well we've got this moment pulling clockwise this moment pulling well kind of anticlockwise but they're not directly opposite to each other here's our pivot here by the way the moment use to this one is just L * W1 that's nice and easy but here it's not as simple as T * L over two like we saw earlier any moment is equals to the force times the perpendicular distance from the pivot to the forces line of action what does that even mean well if I drew the forces's line of action right here here's our tangent and I extended it it would extend out that way it would extend out that way all that we're showing is the direction that the force is actually pulling in so what distance is perpendicular from this line of action to the pivot well it's not from here to here because of course that wouldn't be perpendicular to the line of action instead it's going to be this here can you see I've just drawn a line that is 90° perpendicular to the line of action to the pivot that's my distance there now usually what you'll be given is this angle here I'm going to call that Theta now you could spend ages thinking about okay well where does Theta fit to this triangle here and then where's the distance and all that jazz but what you'll find ultimately is that in order to find out the moment due to this it's going to be the force times the distance times cos or sin Theta so actually more often than not what we can just do is figure out hm well actually the amount of this tension that's pulling upwards perpendicular to the beam that's actually going to be T cos Theta all we're doing is finding out how much of the total Force pulling in that direction is being used to balance this moment here not all of the tension is going to be used if you don't know how I got to this have a look at my easy vector trick video and that will sort you out on that so now it's just as simple as saying well T cos Theta * L / 2 equal W1 * l so the moment due to the hanging basket here is equals to the moment of the tension that is perpendicular to the distance to the pivot here sometimes you'll have forces that are in completely different direction to each other let's look at a children's roundabout uh let's put some handles on there I'm going to say the radius of this roundabout is R let's say that we have Jimmy pushing with F1 and then we have Julie who's pushing in the opposite direction with F2 now if we draw in the perpendicular distances from the force to the pivot we end up with these what you'll find is that these forces are are 90° to each other they are perpendicular to each other but the same still applies F1 is trying to push the roundabout round anticlockwise F2 is trying to push it clockwise last thing you'll come across is Top Lane put simply if you have something like a wardrobe and providing that there's our pivot by the way and providing that the center of mass which is usually right in the center itself is has not gone past the pivot point then it's not gone to Top over as soon as this Center of mass moves over past the pivot point then it's going to topple over because of course the moment due to the center of Mass isn't going to be pulling it anticlockwise anymore but actually is going to start turning it clockwise the last thing that you need to know about when it comes to moments is the idea of couples let's say that you have a steering wheel and usually when you're supposed to turn a steering wheel your hands are supposed to be at 10 and two but let's pretend that your hands are here and here opposite sides of the wheel if I wanted to turn right then my left hand has to go up and my right hand has to go down but I should be pulling with the same force with each hand now of course the pivot is right in the middle here but my hands are two R apart that's twice the radius or twice the distance from my hand to the pivot the moment of a couple is equals to the total moment or the sum of the moments but that's actually not how we Define it if we actually try and figure out what moments we've got going on here obviously we've got f * R plus f * R both of them are pulling this one's pulling clockwise this one's pulling clockwise as well this is not in equilibrium by the way that's probably something I should have said earlier system are not always in equilibrium it's only when we talk about things that are in equilibrium that the moments are equals to each other so of course that's going to be F + f r what you'll notice is that equals to 2 F but how we actually Define it is saying it's one of the forces times distance between forces so that's going to be f * 2 R which again gives you two frr so it's a bit of a weird definition but that is the definition that you need to know so I hope you found this video helpful if you have make sure you give it a like and I'll see you next time