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# Center of mass

## Video transcript

earning I will now do a presentation on the center of mass and the center of mass I hope hopefully is is something that will be a little bit intuitive to you and actually has some very neat applications so in in very simple terms the center of mass is a point let me draw an object let's say let's say that this this is my object let's see it's a ruler and so this ruler it exists so it has some mass and my question to you is what is the center of mass and you say Sal well in order to know figure out the center of mass you have to tell me what the center of mass is and what I tell you is the center of mass is a point and it actually doesn't have to even be a point in the object it and I'll do an example soon where it won't be but it's a point and at that point for dealing with this object as a whole or the mass of the object of the whole we can pretend that the entire mass exists at that point and what do I mean by saying that well let's say that the center of mass is here and I'll tell you why I picked this point because that is pretty close to where the center of mass will be if the center of mass is there and let's say that the mass of this entire ruler is I don't know 10 kilograms this ruler if a force if a force is applied at the center of mass let's say 10 Newtons right so the mass of the skillet of the whole ruler is 10 kilograms 10 kilograms if a force is applied at the center of mass this ruler will accelerate the same exact way as would a point mass let's say that we hit just hit a little dot but that little dot had the same mass 10 kilograms and we were to push on that dot with 10 Newtons in either case in the case of the ruler we would accelerate upwards at what force divided by mass so we would accelerate upwards at 1 meter per second squared and in the in this case of this point mass we would accelerate that point when I say point mass I'm just saying like something really really small but it has a mass of 10 kilograms so it's much smaller but has the same mass this ruler this would also accelerate upwards with a magnitude of 1 m/s squared so why is this useful to us well sometimes we have some really crazy objects and we want to figure out exactly what it does and if we know its center of mass first we can know how that object will behave without having to worry about the shape of the object and I'll give you a really easy way of realizing where the center of mass is if the object has a uniform distribution when I say that it means you know the lissa I mean for simple purposes if it's made out of the same thing and that thing that it's made out of its density doesn't really change throughout the object the center of mass is RIT is will be the object's Geograph it's geometric Center so in this case this is all you know ruler is almost a one dimensional object we just went half way the distance from here to here the distance from here to here is same as the center of mass if we had a two dimensional object let's say we had like this triangle and we wanted to figure out its center of mass it'll be the center in two dimension so it'll be something like that now if I had another situation let's say I had a oh I don't know let's say that I have this square that's thick enough for you to see let me draw a little thicker let's say I have the square but let's say that half of this square is made from let me see half of the square let's say this half of the square is made from lead let's say this half is made from lead and let's say the other half of the square I don't know it's made from something lighter than lead it's made of styrofoam that is lighter than lead so in this situation the center of mass isn't going to be the geographic center I don't know how much denser lead is in styrofoam but the center of mass is going to be someplace closer to the right because this this object does not have a uniform density and it will actually depend on how much denser the lead is and the start which I don't know but hopefully that gives you a little intuition of what the center of mass is and now I'll tell you something a little more interesting every problem we have done so far I actually made or we actually made the simplifying assumption that the force acts on the center of mass so if I have an object let's say the object that looks like a horse that's let's say that object if this is the object center of mass I don't know where the horses center of mass normally is but let's say a horse the center of mass is here if I apply a force directly on that center of mass if I apply force directly at that center of mass then the object will move in the direction of that force with the appropriate acceleration I mean we could divide the force by the by the mass of the entire horse and we figure out the acceleration in that direction but now I will throw in a twist and actually every problem we did every all of these Newton's laws problems we assumed that the force acted at the center of mass but something more interesting happens if the force acts away from the center of mass so let me see actually let me actually take that ruler example I don't know I even drew the horse if I have this ruler again and this is the center of mass as we said any any force that we act on the center of mass the whole object will move in the direction of the force it'll be shifted by the force essentially but now this is what's interesting if that's the center of mass and if I were to apply a force someplace else away from the center of mass let's say I apply a force here I want you to think about for a second what will probably happen to the object well it turns out that the object will rotate and so you know think about where on the space shuttle or we're in deep space or something and if I have a ruler and if I just push at one end of the ruler what's going to happen am I just going to push the whole ruler or as a whole ruler going to rotate and hopefully your intuition is correct the whole ruler will rotate around the center of mass in general if you were to throw a monkey wrench at someone and and I don't recommend that you do but if you did and and while the monkey wrench is spinning in the air its spinning around its center of mass some same for a knife that's you know if you're a knife catcher that's that's something you should think about that the object when it's in a when it's when it's free when it's not fixed at any point it rotates around its center of mass and that that's that's very interesting so you could actually throw random objects and that point at which it rotates around that's the object center of mass that's that's the experiment that you should do in an open field around no one else now with all of this and I'll actually in the next video tell you what this is when you have a force that causes a rotational motion as opposed to a shifting motion that's torque but we'll do that in the next video but now I'll show you just a cool example of how a centered the center of mass is relevant in everyday applications like high-jumping so in general you know we let's say that this is a bar this is a side view of a bar right then this is the thing holding the bar and a guy wants to jump over the bar his center of mass is you know most people center of mass is around their gut I think evolutionarily that's why our gut is there because it's close to our center of mass so there's two ways to jump you could just jump straight over the bar kind of like a hurdle jump in which case your center of mass would have to you know cross over the bar and we could figure out this mass and we could figure out how much energy and how much force is required to propel a mass that high because we know projectile motion and we know all of Newton's laws but what you see a lot in the Olympics is people doing a very strange type of jump where when they're going over the bar they look something like this their backs are arched over the bar that's not a good picture but what happens when someone arches their back over the bar like this hope you get the point this is the bar right here what's interesting when when if you took the average of this person's density and figure out his geometric center and all of that center of mass in this situation if someone jumps like that actually travels below the bar because the person arches their back so much if you took the average of the total mass where the person is their center of mass actually goes below the bar and because of that you can clear a bar without having your center of mass go as high as the bar and so you need less force to do it or another way to do it another way to say it with the same force you could clear a higher bar hopefully I didn't confuse you but that's exactly why these high jumpers occur arch their back so that their center of mass is actually below the bar and they don't have to exert as much force anyway hopefully you found that to be a vaguely useful introduction to the center of mass and I'll see you in the next video on torque