On a pool table, energy is always conserved. Kinetic energy is mostly conserved (kinetic is moving energy, more accurately KE = one half of mass times velocity squared or 1/2mv^2). This means that once you hit the cue ball, it is going to continue to move at a constant rate for quite a while unless it hits something, in which case the cool stuff happens.
Friction does happen a little bit, which means if you it the cue ball very lightly, it will stop before anything good (or bad) happens. But remember its rolling friction, mu-k is about .002. If you give the ball a good solid thwack, it will keep going at a good clip for a good bit.
Collisions between balls are almost perfectly elastic (e = .99). This is handy on the straight in shot, aim dead center on the cue ball, line up the cue with the target ball, and give the cue ball a good sharp tap. The cue will be given an impulse that makes it move straight towards the target ball. When it collides with said ball, all of it's momentum will be transferred, causing the target ball to drop neatly into the pocket, while your cue ball comes to a complete stop right at the site of collision, and you don't scratch.
All collisions except the dead on ones occur at 90 degree angles. So if the cue ball strikes the target ball a little to the left of the center, the target ball will go zipping off a bit to the right, and the cue ball will continue a bit more to the left, with the angle between them at 90 degrees. This means you can make a lot of non-straight in shots easily, but if you aren't careful you can end up sinking both the target ball and the cue ball.
If you are really into it, you can figure out exactly where you need to hit the target ball to make it go in a certain direction. The equation is: vtarget=(n*vcue)n, where n is the unit normal vector between the centers of the balls when they touch (n= Ptarget - Pcue)||Ptarget - Pcue||) and '*' is the vector dot product. Note that v and n are vector quantities.
Orignal From: How to Play Pool Mathematically
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