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Rotational Inertia - Balancing a weighted stick

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Today we're going to look at some demonstrations involving the concept of rotational inertia. Now first of all let's review the concept of inertia. Inertia is a property that we associate with an object that deals with a resistance to a change in a state of motion; that particular property is the mass of the object. Now rotational inertia is the resistance of an object to a change in the state of rotational inertia. That does depend on the mass of the object, but it depends upon something else as well, and we're going to find out by looking at some demonstrations. Now the first one is one that you probably played around with before and that's balancing a pole on your fingers. Its actually very easy to do this you just make small corrections with your hand and you can keep the pole balanced. Now it stays balanced because of something else we learned in a previous demonstration. And that is by moving my fingers I'm keeping the center mass of the pole directly over the point of support. As long as I do that it's not going to fall. Alright, now let's make it even easier. I'm going to do that by putting a clamp near one end of the pole. This will increase the mass of the pole quite a bit, but it will do something else that we're going to see. Now here's a question, will it be easier to balance this at the weighted end or close to the weighted end, or, with the weighted end far from the point of support? Well let's try both ways. With the weight close to the point of support or the axis of rotation I can balance it, but I have to make very big movements with my hand in order to do that that's because the pole is moving very quickly and so I have to respond very quickly. It's a lot easier if I do it this way, I don't have to make the motions with my hand to make it quicker or much slower. And that's because the pole has a tendency to rotate much slower. Why is that? Its because the rotational inertia of the pole is greater when I balance it like this than when I balance it like this. Now the mass hasn't changed what has changed is where the mass is. The further the mass is distributed from the axis of rotation the greater the rotational inertia that it has. And therefore the greater the resistance to a change to a state of rotational inertia. Let's look at another example of that. This one is a little similar to what you might have seen some circus performers do balancing stacks of plates on a long pole. Now I'm not going to try that, but I'm going to balance something on this platform. Its fairly easy to balance as it is but it should be even easier far from the point where I'm supporting it. So I'm going to put these sawed off soda pop bottles filled with water on the top and balance it on my fingers and I can just stand here and this is fairly easy to do. Now my camera man is pretty nervous right now because he is wondering if I'm going to drop this on his camera, but actually I'm just exaggerating I can do pretty much what I want to with this. I just have to be careful when I bring it back down again, because that's the point where I'm most likely to tip the thing over and drop it. That's because I moved the point of the mass far from the mass close to the mass which then is more difficult to keep it balanced. Some other examples of this that you may have seen or one example of this that you may have seen is another circus performer, the tight rope walker. The tight rope walker uses a long pole which extends way out, and what this does is actually a couple of things, it increases his rotational inertia, because there is a lot of mass far from him. And so when he makes, in order to correct his, any slight motions one way or the other its fairly easy to do because with a greater rotational inertia he tends not to rotate very quickly. The other thing it does relates to something that we've studied before and that is the position of his center of mass. You probably noticed that these poles are very long and they droop way down on the ends, as a result they pool the center of mass of the man and the pole downward. You know from what we learned before that by bringing down the center of mass that increases the stability of the system.


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