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Add assorted calculated

hi welcome to the statics tutorials so let's look at calculating some moments with some different cases with two-dimensional systems so in the first case we just have a bar and then we have a single force of 251 Newtons at a distance of 0.3 meters from a the whole bar is 1 meter so it's going to also be 0.7 meters from B the force of 251 only goes in the y-direction so using the method for 2d we'll have this force in the y-direction times this X distance and that'll give us the moment about a now we have to decide is that going to be positive or negative so if we try to make it positive our fingers are going in the opposite direction of the 251 if we make our finger negative going into the or thumb negative going into the board then we can put our fingers in the direction of the 251 so looks like this moment created by the 251 Newtons is negative about a and then just doing this calculation minus sign in front because it's a negative moment not because it's a negative force negative moment 251 Newton's times two point three meters so remember this is forcing Y distance in X the force and the distance always have to be perpendicular and this gives us negative seventy five point three units of just Newton's times meters two Newton meters if we want to calculate the same moment generated by the force but about a different point we could pick B and then in this case we have to figure out the sine as well so over here at B if we make our finger go in the positive direction then our our fingers here are going in the same direction as the 251 Newton so this is a positive moment so the moment about B is positive 251 Newton's times point seven meters gives us a hundred and sixty-seven Newton meters now again if you prefer to think about clockwise and counter clockwise just draw the diagram stab your paper here with your pencil or pen push on your pay or in this direction and you'll see that the paper spins around a in a clockwise direction remember clockwise is negative clockwise is negative so that's our negative moment about a and then if you pin your paper here at be just by stabbing in your pen or pencil and you push on your paper over here it's going to spin your paper around on a counterclockwise motion around B and remember that counterclockwise CCW is positive that's where we get a negative moment here and a positive moment here let's look at another system but let's make our force go in the X direction so we have this beam that has a 90 degree angle on it and then we have a force in the X Direction 201 pounds let's calculate the moment about a this is an X force so we need to multiply it by a wide distance and we need to figure out the whether this is a positive or negative moment thumb into the board or into the paper allows you to put your fingers going in the direction of the two of one so this has to be a negative moment Y distance one foot X force to a one gives you negative 201 foot-pounds now let's calculate the moment of the 201 about point be thinking about point B thumb into the board allows us to put our fingers going in the direction of the tool once this is also going to be a negative moment it is still an X force we still need to multiply it by a wide distance the Y distance is still exactly one point zero so strangely enough moment about B is going to be exactly the same as the moment about a for this case minus 1 foot times 201 pounds gives us negative 201 foot bones now let's look at a slightly more complicated example down here so we have a beam that's kind of an inverted T shape and then we have a force that's going in both the X and the y so 751 Newtons at an angle of 30 degrees the horizontal let's calculate our moment about a so we can do this again by breaking this force up into an X component and a Y component so let's look at the X component first so the X component is going to be 750 one times cosine 30 so that's our FX we need to multiply that by a widest insistence that we're going to use and then we need to figure out is this a positive or negative moment so if we're at a thumb into the board allows us to put our fingers going in the direction of FX so this is a negative moment now we need to look at the contribution of the Y so I'm grabbing it from color so we have FY here FY is going to be F sine of theta this is our FY over here in our equation we need to multiply the Y force by X distance this is our X distance that we want to use down here point four five meters so that's our X distance now we need to decide if this is a positive or negative moment thumb into the board allows us to put our fingers going in the direction of FY so this is a negative moment so both of these contributions are negative when we add them up we get 429 newton meters now let's look at this moment about B I'm going to erase my distances so I can reassign them so with our moment about B it's the same thing we need a force in the X for some X is still F cosine of theta so this is our FX and we need to multiply this by Y distance this point 4 meters is still the Y distance we need to figure out a positive or negative sign thumb into the board at B means our fingers go in the FX direction so this must be negative and then let's look at our Y component so I've got FY FY is still F times sine of theta so still 751 Newton's times sine of 30 and then we need to multiply that by our X distance over to B in this case now the 0.5 is going to be our x distance over to B we need to figure out positive or negative sine so looking at B thumb out of the board we come over here allows us to put our fingers in the direction of F Y so this means that this contribution winds up being positive so when we add these two contributions together we get the overall negative 72.4 newton meters thanks for watching