Why does a seesaw need a pivot? The answer to that question is that the pivot prevents the seesaw from undergoing translational motion, while leaving it free to undergo rotational motion. Without a pivot to support its weight and that of its riders, the seesaw would fall. And while two children might find it exciting to jump out of an airplane seated at opposite ends of unsupported seesaw, that idea is unlikely to be popular with their parents. The physics will be fabulous but I'm not going to film it. I'm going to leave that for children who enjoy extreme recess. Instead, I'm going to show you how an unsupported and riderless seesaw moves. Basically, I'm going to throw the seesaw through the air and we'll watch its motion. For obvious reasons, I'm not going to use a large seesaw, I'm not even going to use one as big as this. But even so, even with a small seesaw board, or a pretend seesaw board, I need more room, so, let's go outside and have some fun. I'm going to throw a riderless, unsupported seesaw. Well that sure was quick. But this is video so I can show you that throw again. And this time I can slow it down to one tenth it's original speed. More over, I can make the images of the seesaw linger on the screen so that you can see all the previous images as the seasaw goes through it's travels. Now, because the camera takes 30 frames per second, those images will be separated from one another by a thirtieth of a second. Here we go. The same throw, slowed down to one tenth its original speed, with all the previous images of the seesaws lingering on the screen. Seeing all those image of the seesaw is pretty, but how do we make sense of the seesaw's motion? It turns out that he seesaw is doing two things at once, it's translating and it's rotating. Translational motion. Well, it's center of mass is traveling in the arc of a falling object as though it were a tiny ball located at the center of mass, that's traveling in the arc that we're familiar with for falling balls. At the same time, The seesaw, which is an extended object, is rotating about its center of mass, its natural pivot. And, it's doing these two things at once: the translation motion of a falling object located right at its center of mass, and the rotational object. Motion of an extended object rotating about its natural pivot. Its center of mass. So I'm going to show you that same video again, same throw. Once again, at one tenth normal speed with all the previous images of the seesaw board. In view, but this time, I'm going to show you the arc of a falling object, and I picked the arc just right so that the seesaw's center of mass will travel along that arc, as the seesaw rotates about it's own center of mass. Located on that arc[NOISE][NOISE] A seesaw has it's center of mass located pretty much in it's geometrical center. So, the motion we saw had the center of the board travelling in the arc of a falling object as the rest of the board rotated about it's geometrical center. But not all objects have their centers of mass at their geometrical centers. For example, a mallet, nearly all of the mass of this mallet is in its head. The handle is almost nothing. So, when I throw this mallet The head will travel in the arc of a falling object because the center of mass is, is, is almost dead center in that head. So you'll see that center of mass travel in the arc, and that's the head. At the same time, the handle. Which is almost an insignificant contribution of mass, will rotate about the center of mass, and the arch'll look a little different. So, now I'm going to throw the mallet. Here we go. This rubber mallet has most of it's mass in it's head. Once again, that was very quick. So I'm going to show you the same throw. But this time, I'm going to slow it down to one tenth its original speed. And I'm going to let all the previous images of the mallet linger on the screen. So you can watch the path the mallet takes. And its orientation while it's taking that path. It's already pretty obvious that the mallet is following the arc of a falling object as it's rotating. But just to make that crystal clear. I'm going to show you the same throw again, one-tenth its original speed, with all the images of the mallet lingering on the screen, but this time I am going show the arc of a falling object that travels along in the path taken by the mallet's center of mass[BLANK_AUDIO][SOUND]. So you see, when you throw something, and it becomes a falling object. That is, it's experiencing only one force, its weight. Its motion is actually fairly simple. The object's center of mass travels in the arc of a falling object. As though it were a simple thing like a falling ball. At the same time, the rest of the object may be rotating about that center of mass. The object's natural pivot. So the object is doing two things at once. It's translating in the arc of a falling object as it's rotating in the manner of an object that's just simply free to rotate about its own natural pivot. Its center of mass. This may look like an ordinary beach ball, but it's not. Watch how it moves. It's hard to catch. [laugh] Why does this beach ball move in such a crazy manner? This beach ball has its center of mass located far from its geometrical center. There's a container over here on the side of the beach ball that's full of water so that the most, most of the mass of the ball is located here where I can touch. As a result, the center of mass is here on the surface of the ball. And when I throw the ball, and it becomes a falling object, it's that center of mass that travels in the arc of a falling object. The rest of the ball comes along for the ride. And it rotates about its center of mass, it's natural pivot. And therefore about one surface, one side of the ball. So that wobbly motion you're seeing is the ball rotating about the side of the ball, it's natural pivot where the center of mass is located. You can begin to locate a small object's center of mass by setting it on a surface to support it's weight and then giving it a spin. It naturally spins about it's center of mass. So, what I can say in, for this basketball is that the center of mass of the basketball lies somewhere on this rotational axis. It's spinning about a line, passing from top to bottom of the ball, and the center of mass is located on that line. I can't tell you for sure where along that line is unless I rotate the ball and spin it again, rotate the ball and spin it again, but eventually, I could pin down the fact that for a basketball, the center of mass is pretty much dead center in the geometrical center. That's true of a basketball. But not so true for knife. How do you find the center of mass of a knife? Give it a spin. It's right about there. It's somewhere, that's the point that's staying put as it spins. It's spinning about that point. So I can tell you the center of mass is somewhere ...between my two fingers. To pin it down further, I'd have to spin the knife about another axis. Can I do it? Ooh. I can. So now I've really pinned down the center of mass of the knife. It's really right there in the middle of this metal piece. Well, for a seesaw, you do the same thing. So here's a seesaw board. You give it a spin. The point that's trying to stay put is right about here. So that's, that's the center of mass. Somewhere between my fingers. And that's where the pivot goes when you make the seesaw into a real rideable seesaw. And I can pull one of those up. Here it is. The rideable seesaw if you're very, very small. Is supported right at its center of mass, and therefore pivots naturally about that point. So we're supporting it right at its center of mass, and allowing it to undergo rotational motion about its own natural pivot. When examining rotational motion, it's technically necessary to specifiy the center of rotation. That is, the point about which all the physical quantitites of rotational motion are defined. We're free to choose that center of rotation. But some choices are better than others. For example, if I'm rotating like this and we want to describe my rotation as simply as possible using the physical quantities of rotational motion, the most obvious choice for a center of rotation about which to build our language is my center of mass, 'cause that's the point about which I'm pivoting. So, in this case, we define the center of rotation as located at my center of mass. So for example, my angle of velocity now is about 90 degrees per second up, remember the right hand rule, about my center of mass. So about my center of mass, is pinning down the center of rotation about which our language is built. But if I'm rotating not about my center of mass, but about my thumb, watch this. Here we go. I can pivot about things other than my center of mass. I need help to do that. But I can do it, and I'm now pivoting about my thumb. So, it makes good sense to define that as our center of rotation and to say that I am currently rotating. My angular velocity is about 90 degrees again, up, about my thumb. That's the center of rotation. Well By now I hope you can see that while choosing a center of rotation is necessary to define the physical quantities of rotational motion, stating that center of rotation explicitly every time you use 1 of those physical quantities is, is a nuisance, and I'm going to stop doing it. Instead I'm going to assume that the center rotation that we have in mind is obvious, unless it's not, in which case I will say it. So, for this case of a seesaw mounted with a pivot passing right through its center mass, its own natural pivot, that is an obvious choice. For our center of rotation. Right here in the middle of the board where the pivot passes through the center of that board. The board's center mass. That's the obvious choice for the center of rotation. And it will assume for the remainder of this story, that every physical quantity of rotation is defined about that point. So, instead of adding language now to all our physical quantities of rotation for the seesaw. Let's put some riders on it. And that's the job for the next video.
