- #1
heyheyhey27
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Say you have a convex 2D polygon with a set of vertices rotating on a flat surface. Given the coefficient of friction and the coordinates of each vertex, how can you determine the torque from friction on this polygon? I'm looking more for an algorithm than some big equation, as this is something I'm going to add into my physics engine for a game. For that reason, an approximation would be acceptable as long as it takes a short time to compute.
I had the idea of splitting the polygon into triangles by imagining lines drawn from the center of the polygon to each vertex, and finding the torque on each triangle rotating about its vertex (the one that is at the center of the whole polygon), but I can't figure out how to get the torque for an arbitrary triangle. I know that to do this for a circle, you just integrate F * dr from 0 to the radius, but I can't figure out an analogue for triangles.
I had the idea of splitting the polygon into triangles by imagining lines drawn from the center of the polygon to each vertex, and finding the torque on each triangle rotating about its vertex (the one that is at the center of the whole polygon), but I can't figure out how to get the torque for an arbitrary triangle. I know that to do this for a circle, you just integrate F * dr from 0 to the radius, but I can't figure out an analogue for triangles.