Rotational friction on a surface

AI Thread Summary
To determine the torque from friction on a convex 2D polygon rotating on a flat surface, an algorithmic approach is suggested rather than a complex equation. Dividing the polygon into smaller triangles can simplify calculations, allowing for an approximation of torque based on the polygon's vertices. By treating contact points as points in contact with the plane, the friction force can be modeled as opposite to the motion, and the moment of these vectors can be used to calculate torque. While a detailed model of friction is complex and considers object flexibility, a simpler approach is sufficient for game physics. The focus should be on achieving realistic behavior without requiring high accuracy.
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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.
 
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A good plan here is to divide your polygon into many small pieces, not a few large ones.

As the size of the pieces gets smaller, the rotation of each piece becomes less significant compared with the translation of the piece around the center of the whole polygon.

I guess that for your game you want something that behaves in a "sensiible" fashion but it doesn't have to be super-accurate. You could probably get away with assuming the contact was just at the vertices considered as a set of point in contact with the plane. Find the vector that gives the linear motion of each point, assume the friction force is in the opposite direction to the motion, then take the moment of the vectors to find the torque.

An accurate model of the friction for this sort of situation is quite complicated, because you have to take account of the flexibility of the objects that are in contact. The simple Coulomb model of static and dynamic friction doesn't apply. But for a game, I don't think you need to get into that much detail.
 
Thanks! I'll play around with that to see if it appears realistic.
 

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