Center of Mass
Date: 02/22/99 at 14:06:54 From: Genevieve Gallagher Subject: Center of Mass My question is: Find the center of mass of a thin plate of constant density covering the region bounded by the parabolas y = 2x^2-4x and y = 2x-x^2. I'm really close to getting this problem but I can't ask my teacher because I'm homeschooled, so please help! I've already found the x coordinate of the center of mass by dividing the Moment about the y-axis by the Mass. I know that you find the Moment about the x-axis in a similar way, but I cannot figure out what way that is. My textbook only gives examples of finding the moment about the y-axis. Thank you. Genevieve
Date: 02/23/99 at 12:08:38 From: Doctor Peterson Subject: Re: Center of Mass I'm not sure which method you are currently learning for moments; the most general method is to integrate y dx dy over the region to get the moment about the x axis, and integrate x dx dy to get the moment about the y axis. If you're doing it with a single integral, you'd be integrating x times the area of a vertical strip; that is, x (y_2 - y_1) dx, to get the latter. So the "similar way" is to use x instead of y multiplying the area. But in this case, symmetry makes it unnecessary to bother with that, and I'm sure that is what you are expected to see. The region is symmetrical about the line x = 1, so the center of gravity must be on that line. Symmetry is a wonderful tool for math and science - it saves a lot of work in cases like this. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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