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Finding the Center of Mass of an Irregular Object

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In this demonstration we're going to see how to find the mass of another irregularly shaped object. For the object we're going to use the state of North Carolina. In order to help with this, I'll be using this piece of equipment, there's the nut tied to a string with the pen tied on the end, what I'll be doing is using this pin and the weight attached to it together with the map so that I can suspend the map from the pin, and see where the pin falls. So I'll begin by putting the pin here, but I'm just picking somewhere around Elizabeth City. I hold the end of the pin so that the map is suspended from my hand, so this means that the center of mass of this object will be somewhere across this vertical line. With a marker I'll draw the line on there. Its kind of a rough line, but you get the idea. So we know the center of mass falls somewhere on that line, but we don't know where. In order to find out we need to draw a second line to intersect with the first. So, I'm going to put the pin in somewhere else, somewhere up here around Boone. Suspend it once more, and draw another line and that's enough to find the center of mass which should be the intersection of those two. But, just for good measure we'll do it one more time, to see if the third line also passes through that point. So I'll put this somewhere down around Wilmington and I don't have to draw the line for you to see that the string is passing very close to that intersection point. So no matter where I put that pin it should pass through that particular point. And, let's see where that is. It turns out that it's very close to the city of Sanford. So, if that really is the center of mass of North Carolina, then I should be able to balance the entire state on that particular point. Now when I said that Sanford was the center of mass of the state of North Carolina I was talking about this cut out of the state. Actually the center of mass is influenced by the distribution of mass of an object. And for North Carolina we know we have mountains on the west and that's going to increase the mass on the western and we have bodies of water distributed through the state on various places. So, all of these will affect the actual state of mass of the state of North Carolina.


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