Hippocampus Physics: Plumb Lines

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When someone throws their tennis racket in the air after winning a match, its motion at first glance seems rather complex. But if you look carefully, you can see that the principles we have been studying on motion apply here, too. A single point appears to represent the movement of the entire mass of the tennis racket as a whole. It follows the same trajectory as a tennis ball hit into the air. This point, known as the "center of mass", acts as if the entire mass of the object is concentrated at it. Every object has a center of mass. One way to find the center of mass of a small object is to use a "plumb line." Hang your object from any point on the object and attach the plumb line to that point. A plumb line consists of string with an attached heavy weight and it hangs perpendicular to the earth's surface. A line drawn lies along the plumb line will pass through the center of mass of the object. Repeat the procedure choosing a different attachment point and draw a line along the second plumb line. The center of mass of all these objects lies at the intersection of the plumb lines. If an object is symmetrical and uniform in density, it's easy to guess its center of mass. For example, where do you think the center of mass of this meter stick is? That's correct, it's at the 50 cm mark. The center of mass of all these objects is located at their geometric center. Where is the center of mass of this flat map of the contiguous 48 states? If you need to convince yourself of this, you can print the map on heavy stock and use the plumb line method. It is not always possible to use the plumb line method. We need an analytical method for determining the center of mass. Let's start with a system consisting of two discreet particles along an axis. The center of mass of the system in one dimension can then be defined in terms of the masses of the particles and their positions along the x-axis. Now let's try some examples.