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I would like to obtain a graph of the potential energy of a polygon under rotation, given that it is proportional to the vertical distance from the centroid to the "floor". I have made the following attempts: given the polygon enter image description here

i have obtained the graph below enter image description here

(ignore the bottom part and the angles). Of course, I should expect a continuous curve, but I'm not getting one... I've obtained this curve using calculations. Any help?

Ray Bern
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  • Explain how the polygon is being rotated. – amd Mar 15 '18 at 17:22
  • Rotated how it would rotate on a table. The angular speed is not relevant for me – Ray Bern Mar 15 '18 at 17:30
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    Looks like you had the right idea, but without seeing your actual calculations, it’s hard to say where you might’ve made a mistake in computing the last to segments. – amd Mar 17 '18 at 06:47
  • I finally managed to solve the problem. The curve above is completely wrong. The idea the solution is that the potential energy of the curve depends on the vertical distance of the centroid to the "floor", and since the centroid rotates around a vertex, it describes a circular motion. Hence it is a curve of the form $a\sin(bx+c)$ and we just need to plug in known values to find the parameters. – Ray Bern Mar 19 '18 at 15:40

1 Answers1

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I finally managed to solve the problem. The curve above is completely wrong. The idea the solution is that the potential energy of the curve depends on the vertical distance of the centroid to the "floor", and since the centroid rotates around a vertex, it describes a circular motion. Hence it is a curve of the form $a\sin(bx+c)$ and we just need to plug in known values to find the parameters. The resulting curve (much nicer) is the following: enter image description here

Where the angular speed with respect to the center of mass has been kept constant.

Ray Bern
  • 627