hello everyone welcome back to another engineering statics lecture video in this lecture video we're going to be moving on to something very special called moments so sit back relax again i hope you guys are all doing well hanging in there and let's begin so moments of a force again before we've always talked about forces that act at the same point if everything's acting at the same point no rotation occurs however we said that if forces do not act at the same point we actually have rotation now the best way to show that is through an example with a box this is something very intuitive a lot of you guys know what exactly is going to happen with this box when i start to apply forces so if i were to take my box and i were to apply force at the very bottom of the box well we actually have two mechanisms the first one is perhaps the most simplest to imagine is we have sliding so we know at the bottom of this box we have a frictional force that's going to try and counteract any movement i put onto the box now if my force that i'm putting on exceeds the frictional force now friction is something we're going to talk about later but friction is capped so if my force that i'm applying exceeds the frictional force while my box is actually going to start to slide so that's going to be the first mechanism now if i were to take that force and start moving it up the box we introduce or we are introduced to our second mechanism which is going to be tipping so if the applied force p starts to act at a significant distance above of course we know that the box is going to tip and in this particular case the box is going to tip about a very specific point in this case that is called point o what happens is with this force we actually created something called a moment because this force did not act through point p again we're now in a situation where we have forces that do not act through a point now a moment is a quantity used to describe the ability of a force to cause rotation of a body about a specified point so the first key here is that moments are not general some moments can be general we're gonna discuss that in week five but for the majority of the cases moments are always specialized about a point i wouldn't say that the general moment is something i would say the moment about this point is this the moment about this point is this etc etc so the moments depend on which point you want to take them about now the formula for moments in two dimensions it's actually really simple we're going to take our force and multiply it by a perpendicular distance so the only thing that you guys actually have to remember is that this distance that we're multiplying our force by it's going to be perpendicular now if i'm taking force and multiplying it by distance we know that moment's going to have units of something like newton meters or if you're in the states pound feet something like that now again the only thing i really want to stress is that perpendicular distance so if we look back at our figure here if i were to draw a line through that force well we know that that perpendicular distance is simply going to be that vertical distance which i call d perpendicular so we're going to talk a little bit more about that specific one but as we can see moments in two dimensions they're actually really simple uh this week again we're discussing moments of a whole so we're going to go from 2d to 3d the 2d moments very simple this video hopefully it's rather short but when we get to next week 3d moments or i guess the next video that's where it starts to get a little bit more complex so if you guys are saying clayton this is pretty easy i'm having a great time well good i'm glad you're having a great time but don't get too comfy so before we get into 3d moments let's talk about something called the principle of transmissibility now this is actually really nice because it helps answer a lot of questions i find students who are experiencing moments for the first time have now what this principle actually states is that if a force acts along a rigid body the effect of the forest is actually the same throughout its line of action now you guys may be kind of doing that like blinking meme and saying clayton what the hell does that mean well it actually means this let's say i had this situation right here where i have kind of an l-shaped bar and i want to take the moment about point o the first thing that students have trouble with is finding that perpendicular distance because they don't really know what it is they'll say if i measure directly from p and go straight up well i get my distance to a point but that point isn't 0.0 so it's this actually the distance that i use and the answer is yes because what the principle of transmissibility means is that the effect of this force will be the same along its line of action so what i can do with my force is i can draw its line of action extending indefinitely and then it allows for a very easy determination of that perpendicular distance so as we can see here the perpendicular distance in both cases is going to be the same however students much prefer directly measuring to the point rather than measuring to some random point in the object so that's all that this is now the second thing students seem to have trouble with is when we take our situation and we apply a force that's at an incline something like this now there's two things that can kind of happen here the first is students will go okay well i know that the perpendicular distance is going to look something like this and i can solve that through trigonometry well of course you can you can definitely solve this through trigonometry but i'm going to be honest with you guys don't it starts to become quite time consuming and again the name of the game and exam type scenarios is speed remember that cars from disney i am speed that's what you guys should be doing right before the exam because you guys want to try and finish as fast as possible now how do we counteract this well the easiest way is to actually use vector components so what i can do is i can take my situation that i have here on the left and i can say well that's actually the same as this situation on the right now this is actually very nice because if we look at force py i can extend it up using the principle of transmissibility and then i can say that my perpendicular distance is simply going to be dx and i can do the same thing for component px i can extend it using the principle of transmissibility and then i can find that perpendicular distance d y now the question becomes okay okay moments simple all i do is take my force multiply by a perpendicular distance yes that is it it is simple but there's one last thing to keep in mind moments are vectors they're just like forces they are vectors and remember that vectors have two things first is the magnitude which is going to be the force times the distance but they also have a direction now when we talked about forces we said that vertical forces for instance if they're going upwards they're positive and if they're going downwards they are negative well moments follow kind of the same type of logic where if we have a counterclockwise rotation we say that it's a positive moment and if it's a clockwise rotation we say it is a negative moment so this is in 2d counterclockwise is positive clockwise is negative now you guys may be saying clayton how exactly do i tell if it's going to be a clockwise or counterclockwise moment well the best thing i do in exams and i i was a kind of a very proud instructor when i walked through the exam and i saw a lot of students doing that is i just use my pencil so for instance if i'm looking at px right now and i want the moment about o what i would do is i would hold my pencil and where i'm holding my pencil that is going to be 0.0 and we know that px acts horizontal so if i were to come through as we can see my pencil here starts to rotate clockwise now if i were to do the same thing for py again i'm going to take my pencil i'm going to hold it at the point i want to measure and then i'm just going to apply the force py in this case goes upwards so once i start pushing my pencil we can see that it starts going counterclockwise that's what i do it's very simple and it's nice because in the exam you have your pencil ready it's very very quick to kind of do the rotation if you don't have a pencil during the exam well i'm sorry but i think you got bigger problems to worry about than to try and find a moment so if i were to take the moments about point o using these two components i would get the following equation for my moment it'd be negative px times dy so again the force times the perpendicular distance and again when we did the moment we saw that px was clockwise therefore we have the negative sign and we go plus py times dx again for py once i did my moments we said it was counterclockwise therefore it's going to be positive so it's that sign convention you guys need to worry about other than that moments are actually that simple so yeah that's it for this video i want to thank you guys so much for listening i really appreciate it i hope you guys have a wonderful day and i will see you in the next video you