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We don't want to beat this up, but we need to stretch. So let's do that. A point of contact will be a geometric point. (The ball is quite inelastic.) As long as all the balls are on (in contact with) a flat table, they will have a contact point somewhere on a circle described by a plane parallel to the table top that includes the center of the ball. That's for a ball that is still. The same applies to a moving ball, but there is a "dynamic" included as the ball is in motion. At the instant of contact (and, again, we're talking inelastic contact creating a single point of contact), the contact point will still be somewhere on that circle about the middle of the ball that is parallel to the surface of the table at the moment of contact. Remember that a moving ball can contact one or more other balls at the same time. We've left out the possibilities where a ball has left the table, as in a situation where a player elects to accidently ends up with some kind of jump shot, or a struck ball leaves the table and strikes another ball. All balls stay in contact with the table.

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Q: What area of a snooker ball makes contact with another when they touch?
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