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Center of Mass and Stability

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We are going to be looking at several demonstrations that have to do with center of mass and how the position of the center of mass deals with an object's stability. Let's begin with a parlor trick you have probably seen before. Take a fork and a spoon, interlock them, slip a match in between the tines of a fork, and balance it on a glass, or in this case a beaker, and you can make the whole combination balance there. The reason this works is because the center of mass is right at the lip of the beaker, so the point of support is directly below the center of mass. The reason the center of mass is at that particular point is because its not in the fork or the spoon, but at a point right below it. Now, by symmetry since the fork and the spoon are almost the same shape, the center of mass is along a line approximately here, but since the spoon extends way out and the fork extends way out, the center of mass will be way down here. So the center of mass doesn't have to be within the object itself.

Let's look at another example. Here we will be using our 2d NCSSM student, call him 2d. We are going to put some weight on 2d's hands, and balance 2d right there on the top of the head. Its very easy to balance. Now, like the fork and the spoon we have a lot of the weight extending outside, away from the point of support. Because of the symmetry of the object, we know the center of mass will fall below on a vertical line, and it will be quite a ways down because most of the weight is on the hands. Now this is a very stable object, so now we want to talk about why it is stable and how that relates to the center of mass.

I'll begin by looking at a different object where it might be easier to see what is going on. I'll just use this support for another piece of equipment. It has a wooden base and a metal rod. Sitting like this it is very stable, it is very hard to make it tip over. But if I put it like this, its essentially impossible to keep it from tipping over. That has to do with what happens to the center of mass when the object tips. The center of mass in this object is in the wood. In order to tip the object, notice the center of mass has to rise first. Its going to rise before it finally starts to fall over again. It has to rise quite a large distance. However, if the object is like this the center of mass is now up here and as the object starts to tip, the center of mass immediately begins to go downward. So the difference is, if the center of mass has to be lifted, then the object will be more stable. Now, let's take a look at 2d real quickly. The center of mass of 2d is way down here, because that's where most of the weight is. So, I would actually have to pull this to the side like so to raise the center of mass. In fact, I couldn't raise the center of mass far enough to make the object tip over. On the other hand, if I put most of the mass above, the center of mass is above my finger, so when I let go, the center of mass will fall immediately, and would be impossible to balance without moving my finger.

Now, there are a number of toys that work on this principle. Here is one of them, this horseman is plastic, but there is a very heavy weight on the end here. So the center of mass is down here, in fact the center of mass may be close to or within this mass here. In order to make this thing tip over, we would have to make the center of mass go above the top of this stand, which would be impossible without practically pushing it over. We also have this bald headed eagle, which balances on its beak.

Now, if you don't have toys like this at home, its very simple, all you need is a pencil with an eraser and a paper clip. Open up the paper clip, stick one end in the pencil eraser. The center of mass will fall right below a line down my finger.

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