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    <p>Well, my favorite physics book is <a href="http://rads.stackoverflow.com/amzn/click/0471320579" rel="nofollow noreferrer">Halliday and Resnick</a>. I never ever feel like that book is dumbing down anything for me (the dumb is inside the skull, not on the page...).</p> <p>If you set up a thought problem, you can start to get a feeling for how this would play out.</p> <p>Imagine that your two rigid air hockey pucks are frictionless on the bottom but have a maximal coefficient of friction around the edges. Clearly, if the two pucks head towards each other with identical kinetic energy, they will collide perfectly elastically and head back in opposite directions. </p> <p>However, if their centers are offset by 2*radius - epsilon, they'll just barely touch at one point on the perimeter. If they had an incredibly high coefficient of friction around the edge, you can imagine that all of their energy would be transferred into rotation. There would have to be a separation after the impact, of course, or they'd immediately stop their own rotations as they stuck together.</p> <p>So, if you're just looking for something plausible and interesting looking (ala game physics), I'd say that you could normalize the coefficient of friction to account for the tiny contact area between the two bodies (pick something that looks interesting) and use the sin of the angle between the path of the bodies and the impact point. Straight on, you'd get a bounce, 45 degrees would give you bounce and spin, 90 degrees offset would give you maximal spin and least bounce.</p> <p>Obviously, none of the above is an accurate simulation. It should be a simple enough framework to cause interesting behaviors to happen, though.</p> <p>EDIT: Okay, I came up with another interesting example that is perhaps more telling.</p> <p>Imagine a single disk (as above) moving towards a motionless, rigid, near one-dimensional pin tip that provides the previous high friction but low stickiness. If the disk passes at a distance that it just kisses the edge, you can imagine that a fraction of its linear energy will be converted to rotational energy. </p> <p>However, one thing you know for certain is that there is a maximum rotational energy after this touch: the disk cannot end up spinning at such a speed that it's outer edge is moving at a speed higher than the original linear speed. So, if the disk was moving at one meter per second, it can't end up in a situation where its outer edge is moving at more than one meter per second.</p> <p>So, now that we have a long essay, there are a few straightforward concepts that should aid intuition:</p> <ol> <li>The sine of the angle of the impact will affect the resulting rotation.</li> <li>The linear energy will determine the maximum possible rotational energy.</li> <li>A single parameter can simulate the relevant coefficients of friction to the point of being interesting to look at in simulation.</li> </ol>
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    1. COInteresting suggestion, and a very good one; you're right, I do tend to assume that the edges have a maximal coefficient of friction; the problem is that even with the "barely edge contact" situation you refer to above, not all the energy gets transferred to angular momentum; in fact, i doubt that it would be at all more than 50%. To some extent, I'm just hoping to find something that will explain the mechanics of this in a way that a software guy can comprehend. As is, I still tend to think that a rigid body simulation might be the best way to go, but I still want to avoid it...
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    2. CO@McWafflestix, right, I was imagining a bizarre disk that had very high coefficient of friction but no stickiness at all. An absurd item but it does make the point: if you had two disks wrapped in sandpaper that barely kissed as they went past, they would end up spinning very rapidly and moving much more slowly. That's what I mean with "normalizing" above: you can roll all the coefficients up into a single parameter that you could fiddle with until the behavior is interesting to you.
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    3. CO@bobcross: it's an interesting point, and one which is certainly useful for understanding the problem; assuming an infinitely high edge friction coefficient (but no stickiness), two disks which just barely touch while moving past each other would clearly have their velocities averaged and halved, with the remainder of the momentum energy (1/2 the total) going into angular momentum (split between the two). Generally, I'm more interested in accurate simulation than "good enough"; mostly that's because accurate simulation is surprisingly simple, actually, once you understand what's going on.
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