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Limit of Rotational to Linear velocity in pool (billiards)

I wasn't sure whether to post this here or in the maths forum. Please move as applicable, thanks admins.

Hi, I am looking into the physics of pool because I am in the process of creating a set of tutorials for youtube. But I have hit a snag. I am trying to find the limiting angle that a ball can be spun into after deflecting off another ball. (This may not have made much sense so I shall clarify with pictures)

Fig 1.

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In Fig 1, the white ball is travelling vertically is deflected off of the red ball. Since I am assuming perfectly elastic collisions, the white ball will be deflected down the lag line (parallel to the tangents upon collision) and then the top/bottom spin will create the curve depending on the amount of spin upon collision. I already know that the final vector for the white ball is dependant only on spin and not velocity, and the length of the lag line increases with velocity.

As the angle of collision varies, the limiting change of direction varies. So I would like to know what the limiting deflections are, indicated by max top spin and max bottom spin in red.

I am assuming that the cue is flat, i.e played through the ball in a parallel plane to the table, and that the cue tip contacts at a maximum of half way up or down the white ball as indicated in fig 3.

Fig 2.

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I am hoping that the answer is as simple as a line on this next graph due to there being a maximum value for "rotational : linear energy"

Fig 3. Natural Roll.jpg

Thank you in advance for any and all help. <I'm struggling to get the images to work in text nicely>

(the curves on those graphs are just approximations from experience and have not been calculated in any way. I have used cubic Bezier curves with a double strength lag point I.e. P0, P1, P1, P2)