okay, gang, let's begin. if i take this ball and i throw it to the air, almost a nice clean, smooth path, doesn't it? a smooth path. what's the name of that path?

a parabola, that's right. let's suppose i take something like this l shaped and i throw this to the air. nice clean, smooth path? and no, n-o, right? but there's one part of this that does follow. a nice clean, smooth path, as all other parts wobble about it. and that particular point is the point we're gonna talk about today. and that point is called the... center of gravity. center of gravity or center of mass. we talk about the center of gravity as something, honey, we're talking about the center of weight where all the gravity forces seem to concentrate. seem to. we talk about the center of mass. we're talking about the point where all the matter seems to be concentrated. okay? here's a book. where is the center of gravity of the book? the same place the center of mass is, right in the geometrical center. i could find that by drawing a line like this and a line like that, and i could balance it right there. and you know what? gravity's pulling on all parts of that book. okay? but they all average out to be as if it's in the middle. so all i have to do is support it at one place. i don't have to support it all like this.

i can support it at one place. and if i supported it over here, and it balanced, then you know darn well this edge must be very, very heavy, right? 'cause the center of gravity wouldn't be in the center. so the current center of gravity here... [makes sound] there should be. how about the center of gravity in something like this? where would this be? well, we can find it. what we can do is we can hang it up. i can hang it up, and i could draw a line straight down. 'cause i know the center of gravity must be underneath that line. straight down right out the other side. so the center of gravity is somewhere along that line. where along that line? watch this. hang up by another point. well, look at this. that other line was like this. right there. that's where the center of gravity is. and, of course, i could do it by any other point and get the same thing. i come down through here. it would all intercept at that point. that point is outside the object itself, which tells you something. the center of mass of an object doesn't have to be where there's any mass.

where is the center of mass of a hollow basketball? - in the middle of that. - right in the middle. when you throw the ball, it go-- it rotates about its middle. and what's in the middle? nothing, unless you wanna say the air. where's the center of gravity of a doughnut? it's right in the hole. and you take a doughnut, and you toss it to the air, might spin and wobble, but it'll wobble about at one point. and that one point will follow the nice clean, smooth path. take an object like this. where's the center of gravity of this? same type thing again. i can hang it up. somewhere along that line. and i could check that because i could see if it would balance along that line. done accurately. i mean, did a little sloppy. okay, get the idea. let's take another point. okay. see those two lines intersect. guess what's it, gang? i can double check that with one more line. and sure enough... [laughter]

sure enough, all three are right through there. and that's the point where balancing takes place. you get the idea. hey, i take this object and i hold it like this. watch what happens? oh, it falls. that's strange. well, let me hold it like this. it still falls over. let me hold it like this. oh, it's okay. like this, it's okay. like this, it's okay. like this. oh, yacko. how come it topples? because the center of gravity is over here and underneath is nothing. there is no place of support. let's look at that. here's my l-shaped piece of wood. center of gravity is right here.

that means all mother earth pulls down like this. just as if all the weight were concentrated there. but look, there's no support position down here. the last point of support is the corner. and you know what it does? it rotates around that corner. it's just as if i had a little fulcrum here. you people know what a fulcrum is? like in a see-saw, it's the part about which rotation occurs. usually a triangular shape in diagrams. the fulcrum. it's just as if there's a fulcrum there. and it rotates around that fulcrum. and when it does that, it gives rise to a twisting force. it twists. we don't say twisting force. we have another name for twisting force. ends with--starts with t, rhymes with dork. what is it? torque. torque. definition. torque equals-- definition time, gang.

torque equals force times distance. what distance? it turns out the lever distance. i could say distance of lever arm. and that turns out to be this distance right in here, gang. that lever arm distance is always the shortest distance between the point about which rotation takes place and the line of action of the force. it's not the distance between here and here. no, no, no, no. it's the distance between here and the line of action of that force. that force acts all the way down toward the center of world, and the shortest distance is right in here. it'll always be perpendicular, by the way, to the force. see? 90 degrees in here. so that lever arm distance multiplied by this force

gives rise to what? torque. begin with a t, rhyme with dork. try it. torque. that's right. so torques produce rotation. torques will make things rotate. well, strictly speaking, torques will rotationally accelerate things. meaning you have to rest and there's a torque, it'll rotate from rest. or if it's already rotating and there's a torque, it'll rotate at a different speed. so torques tend to change the rotational state of things. and so this thing rotates simply because there's a torque acting on it. that's kind of easy to see, isn't it? how about the center of gravity of people? do people have centers of gravity? answer end with a p. check your neighbor. all people, even them, everybody got a center of gravity, gang.

and guess where your center of gravity is? do you ever wonder about it? is your center of gravity at one place? stand like this. my center of gravity right now is behind here and through here. if you put a barbecue spicket right through here, okay? and i stood like this, and you flip me at-- [makes sound] go really nice, nice, nice, nice. if instead you put the barbecue spicket through here, you-- [makes sound] "say, that dude's wobbling off center." what do you mean off center? off center of mass, so center of gravity, see? when you get your tires balanced, you see some people driving the screeching rubber all the time. they're wearing the tire up more on one side than the other. and pretty soon you are-- going down the road and-- [makes sound] your tire's out of balance. so you bring it to the gas station. the gas station types, they put on a thing, don't they? in that little sea-saw type thing that put these lead weights. what are they doing? they're trying to get the center of gravity where? right along the axle, right along the axis.

and if it's there, it'll rotate nicely. if it's not-- [makes sound] it will pump. so center of gravity. but center of gravity in people varies. because where's my center of gravity now? or now? or now? you see if center of gravity changes, because can't you make yourself like a l shape? let's suppose i stand against the wall over here. i stand against the wall. my center of gravity is where? about in here. how about i bend over, what happens? center of gravity-- you guys see it pop out right out through the shirt? you see that? the center of gravity popped right outside my body. i felt it. you guys do it. yeah, can you feel it moving around in there? try it. --you feel that sucker moving in there. okay? no, you can't feel it. okay. it's an average point. it's an average position, right? but it turns out, when you turn over, the center of gravity does pop forward. how would you like to get a "a" in the course and don't have to do any homework,

don't have to do any exams, automatic "a," scout's honor. be likened. yeah. yeah. next time we meet, we're gonna start-- we're gonna have a line here. people stand up. put your heel against the wall. put your hands above your head. hold ping-pong balls in your ears--reach over. reach--turn, turn, turn, turn. come down and touch your toes, and come on back up and i give you a "a" in the course. with no tricks. no tricks. straight. i mean, no suction caps. [laughter] or no wearing skiis. okay? because what happens? it's sort of like this. you reach over like that, your center of gravity gets over here, yeah? now, what happens? old mother earth pulls down,

but where's the last point of support? right over here, on the toes of your foot. see that little distance, gang? that little distance is what kind of distance? lever arm. lever arm distance. and you got a force, and you got a lever arm distance, what's that give rise to? torque. a torque. and so what's the torque do? rotate out. rotate. so quick, boom, over you go, unless you wear skis or have enormously long feet. [laughter] okay? can you kind of see that? your center of gravity for the average human being will extend beyond the toes when you lean way over. and how can you beat that? so it's not what kind of shape you're in, it's not mind over matter, it begins with an f, gang. physics, yay. so physics, that's right, so try that. and if you can do it, come and get your a. [makes sound] let me say this. it has been done, legit. it has been done.

i have given a's for this. yeah. [laughter] i remember, one time, it was back in the seventies, i did that. i gave an a. it turned out that lady had the longest feet i've ever seen. [laughter] and she was all hips, nothing on top. so she went--bent over, there wasn't much change at all. [laughter] anyway, the lady got her a. and this was back in the seventies, and people were a little different then. you know, the human race is developing all the time. we're becoming more and more developed, more conscious, more sensitive to our fellow human beings, isn't that true? well, i mean, if that happen next time and someone gets an a, how are we gonna feel? "wow. hey, boy, that dude there got a a. "--i might struggle and i might get a d "on the course, "but at least i feel good knowing that one of us is getting an a." wouldn't you feel that way? right? right? right? you say, "one of us made it, man." and you go home at night

and you're flunking all your courses and you got a grin on your face and someone say, "how come you're grinning?" and you say, "'cause one of us is making it, one of us is making it." you know how it was back in the seventies when i gave that lady the a? the class asked me, "is she really getting an a?" "yes, she's getting an a." i said, "scout's honor." and someone, "she's really getting an a for that?" i said, "yes." and guess what they did? ooh, they didn't like it. one of their own. boom, am i glad to see we're developing. isn't that right, gang? [laughter] that's the old days. you know, this center of gravity has to do with a lot of things, like it has to do with, like, your body condition. let me give you-- let me show you what i mean. this is an ordinary woman. where's her center of gravity? right above her head. it's about right here. center of gravity. i mean, it's ol' mother earth pulling down

as if all her weight were there. any torque? no. no torque. she's okay. consider pregnancy. [laughter] what happens to her center of gravity, gang? it-- it's forward. it shifts forward. ol' mother earth pulls down as if all her weight is there and uh-oh. you see this little distance right here, gang? this little distance right in here? you know what that little distance is? lever arm. that's a lever arm distance. see the weight acting down, force? lever arm distance. what's acting on the lady? begin with t, rhyme with dork, what is it? torque. torque. what's the torque gonna tend to produce? rotation. rotation. kwip, boom, she fall over. that's why you see pregnant women, usually their faces are all smashed up with, you know, they're all flat falling on their face, ain't that true? that's not true. that's not true. we are humans. we learn to adjust.

so she does not fall over. instead, she leans back to pull the center of gravity back. she does something like this. she's leaning back a little bit. yeah. now, the center of gravity comes back right over her feet. she is a-okay. see that? brought it back. except...back pains. back pains, gang. it's a very common ailment when women get pregnant to develop back pains, because they pull back like this to adjust for the center of gravity and that is hard on the back. doan's pills. yay. anything this young lady can do to prevent those back pains? check your neighbor. any ideas, gang?

bigger shoes. skis. skis, wear skis. right on, man. you get an a in the course. so all she got to do is wear skis. look at this, gang. [laughter] if she wears skis, she'd be okay. ain't that nice? how many of you, "oh, she shouldn't wear skis 'cause people will laugh at her"? she should instead have a back like this. what else could she do besides wear skis? any other ideas? use a walker. a walker. that's right. she could have a walker around here and she could kinda hold-- or she could have a cane. a cane. she could have a cane, maybe hold the cane like this, right? but then she'd have to keep lifting the cane up. put a roller skate on it. [laughter] and she could kinda-- hey, you're right. any other ideas? she could wear a backpack. backpack. excellent. a backpack. wonderful. what she can do is a backpack. never mind all these stuff here. no skis. all she got to do is hold it around up like that and have it like... [laughter] hey, can you see that?

that pulls the center of gravity back. hey, huh, that would work. backpack would do it. some people say, "wait a minute, though, "as she becomes more and more pregnant, she'd have to put more and more weight in the pack." true or false? answer begin with an f. false. false, very good. check with your neighbor what she could do besides put more rocks in the pack as she gets more and more pregnant. go ahead. she could move it back further, can you see that? she could put little notches on here, right? [laughter] in fact, all of the people say, "when is due day?" right? she can have all the notches. oh, this last notch should be dd, right? drop day, okay? [laughter] just keep moving back, back, back. center--yay. do you ever see the way a pigeon walks? a pigeon that go like this, okay? what's that pigeon doing? every time that pigeon picks up a step, what's he do? he pulls his head back to what? see, it's like having the same here, okay? the pigeon has to readjust center of gravity

with every step. so he does that by pulling back like that, doesn't he? watch that sometime. most birds walk like that, monkeys too. a monkey can lean way over and grab things and move with grace, because the monkey got that big tail and that tail stick up, and that tail makes the center of gravity come over the feet. so the monkey reaches over with both hands. the center of gravity right above its feet, counterbalance, keeps the center of gravity always above the point of support. really nice. see, a lot of animals have tails. remember the dinosaurs with those huge, huge tails? when they stand up and run there, they run-- a great, big body, huh? but the other part of the tail out here, yeah, center of gravity right there. hey, they got to have the-- cut off the tail, what's that dinosaur gonna do? you know, i mean, he can't make it, huh? [laughter] i mean... a pregnant lady. yeah. you're in san francisco. and when you're in san francisco, you're in one of those hills, the famous hills in san francisco. in the famous hills, you have a bunch of trucks.

and these trucks, you say, "how come these trucks don't tip over?" well, it turns out these trucks are loaded differently. this is truck a, truck b and truck c. truck a has its center of gravity very, very low, right here. truck b has a center of gravity right about here. and truck c has it way up about here. which of those trucks will tip? a, b, c, or all or none? check the person you sit next to and see what you think. straight down? yup. straight down? yup, b and c. oh, ah, this is not so good, gang. yeah. which one gonna tip, gang? all of them. how many say all? that's right, all. i got this-- i got the hill a little steeper than i'm used to drawing.

you see, what happens is the-- see there's a little lever arm distance here, a lever arm distance here, a lever distance here, okay? let's suppose i were more careful when i was drawing this and i put this center of gravity here like over here and i-- well, here's the criterion. if i come up from that wheel, if it's anywhere to the right, i'm okay. if it's anywhere to the left, i'm not okay and over-- it's gonna tip. do you kinda see that? some people think if the center of gravity is highest, the more it will tip. not necessarily. it's whether or not it's beyond a point of support, because--let's suppose i had, like, bigger wheels. let's suppose i draw it like this. now, when i draw this, this is what i got to do. as a teacher-type, i have, in my mind, see the line and draw the center of gravity like over here and say, "hey, let's suppose it's really high, gang, like up here."

and some people say, "wow, it's so high, for sure it's gonna tip." but that's not the criterion, is it? you people all know what the criterion is. i don't care how high. it's not how high, it's which way. if it's on this side, what's it do? [makes sound] if it's on this side, the center of gravity is between points of support. isn't that neat? do you see that? any questions? if that truck was on a slope even just a little bit the other way, what would happen? oh, the same truck? yeah, would tip right over. because now, we got-- [makes sound] [laughs] splat. okay? a huge torque. i think of that-- [makes sound] okay? very good, lee. very good. hey, you know, sometimes the easy questions are the hardest to answer. let's suppose some kid asks you, "how come a ball rolls down a hill?"

"--balls always roll down hill, honey, gravity pulling. "you want to gets to the bottom of the hill, gravity is still pulling. don't roll down anymore." you say, "when there's no more hill." the kid will, "why does it roll down the hill when it's on the hill?" and you say, "what are you asking questions like that for?" and the kid says, "because i wonder "about things like that and you're a college type "and i think maybe you can be the one to tell me. "and you would say, "roll down the hill, roll down the hill. hmm." could you guys handle it? could you answer a kid's question like that? let's take a hill here. okay. i don't have a ball but i got a disk, okay? i take the disk and i let it go and sure enough it rolls down. why? why is it rolling down the hill, gang? see this, gang? center of gravity is right here in the center, right? pulling down, but the point of support is over here.

and what's this little distance in here called? lever arm. lever arm. and what's this here? force, right? and--force through a lever arm produces a-- torque. --torque. and what's a torque produce? rotation. rotation. and so we see when we let the ball go-- unless we go mumbo jumbo, then you let go and-- hey. did you guys see that? magnet. not the same disk. what's going on here, gang? there's a magnet in that. you're out in the south seas. you come to an island. you wanna set yourself up with the new people and you take a disk like this and you go, humba, humba, humba, humba, humba. [laughter] follow me, i'll make your crops grow. you guys get out there and tow the fields and i'll humba, humba, humba, okay? come on, gang. what's going on here? any of the guys know? did you ever throw a dice in reno and all the time, man and seven comes up, huh? guess why. it's loaded, honey.

guess where this was made. las vegas, okay? [laughter] see what i got inside there? see that little hole there? inside there is buried something-- begins with l, ends with "ed". try it. lead. and that lead does what to the center of gravity, gang? makes it in the middle? no. off the middle. so the center of gravity now is off center. in fact, when it settles like that, you know that the center of gravity now is what? must be right above-- right on there. must be sitting like that. ain't that neat? can you see that? yay. center of gravity. let's talk about seesaws, seesaws. seesaw in the park, kids playing on the seesaw. the law of seesaws is rather simple. it's just torques like we've been talking about. let's see, let's see what i mean.

is the seesaw balanced right at its center? where's the center of gravity of the seesaw if it balances like that? it must be right here, okay? now, let's consider a couple of kids playing. this couple of kids sit equal distances from the center. why does the seesaw remain in balance? because the kids weigh the same? hmm, yeah. or because the kids provide the same but opposite-- begin with t, end with dorks-- rhyme with dork. torque. dorks. torques, see that? same torque. this kid here got a weight acting down. this kid got a weight acting down. this weight acting down multiplied by that distance gives rise to a torque which tends to rotate at this way.

this weight acting down multiplied by this distance gives rise to a torque that tends to make it rotate this way. and if no rotation occurs, what's the net torque? zero. zero. that means this torque must be equal to this torque. and this torque is the force of gravity acting down multiplied by this distance d. and this torque is the force of gravity acting down multiplied by this distance d. and if fd is fd, same, same, the torques will be the same and the kids get balanced. this is different than the equation we used for energy although it looks the same. and when we talk about work, is force time distance? but in that case, the distance was always the distance along the direction of the force. in this case, for torques it's always the distance

perpendicular to the force. see that? here is a leverage distance. in other words the distance the force moves. so some people get confused and say, wait a minute, i've seen that equation before, but different distance. we can say, this is the perpendicular distance or the perpendicular component of force along the distance, either way. but i think we all know about this. let's suppose this kid goes home and someone takes his place. and it's a great, big, heavy set kid. can a heavy set kid play with a little skinny kid on the same seesaw? yeah. and you all know from experience, yes. a heavy kid can do it. and what the heavy kid does-- the heavy kid sits in here and the kids can still play. the kids can still play because who is providing the larger torque? the heavy kid or the light kid? check your neighbor. watch out for trick questions like this.

who's providing the larger torque? check. how many people say, the larger kid is providing the same torque, that's why it balances. yay. see? the larger kid is pulling down with more force, but through less distance. so there's a greater force, but a lesser distance and if this equals that, they balance and it's okay. let's suppose the large kid is very, very obnoxious and this kid says i ain't gonna play with you anymore. can the large kid play with himself on that seesaw? can he? and the answer is yes. but the larger kid's got to move the fulcrum. what the large kid can do now, okay, he can sit on the seesaw maybe with the fulcrum like this. that's a mystery to a lot of people

as to why he could do that. how can the kid play with no partner by shifting the fulcrum closer? because we know the kid has a big force acting down and there's a small distance here. and that big force times that little distance gotta be equal to some other force times some other distance, but you know what, gang? there's no force on the other side at first thought. is there a force on the other side of the fulcrum? yeah. what is it, gang? where's the weight? the weight of what? board. the board. the board's got weight. where is all that weight concentrated? in the center. right in the very center of the board. so the weight of the board itself pulls down. this distance here, i don't know what it is, it some distance. but let me ask you a question. if you took that distance, i don't know what it is, and you multiply by the weight of the board, you gonna get a number?

that's gonna give you a torque like that. if you take the weight of this kid, very heavy kid times a small distance, you gonna get a number? that's gonna give you a torque like this. is there a way maybe to find out what the weight of the board is, if you knew this particular distance? and then, i want to give you something else to think about too, gang. see this broom? okay. where is the center of gravity of the broom? how many can see where the center of gravity is? is it in about here? all right, center of gravity right there? you see that? okay. here's what i'm gonna do, gang. right through the center of gravity. i got a question for you.

if i put this in the bathroom scale, which weighs more, this or this? or the same? think about that. if you know the answer to that, you know the difference between torque and weight. think about that. catch you next time. yay. [music]