# Billiard physics

#### Entropia

does anybody know of any good sites that explain the physics and geometry of playing billiards (pool) ?

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#### Entropia

yes yes i've tried that.

but it never ceases to amaze me, the websites other people can come across on a topic that i looked up.

but i've got enough.

thank you though! :D

#### Alexander

So what exactly is you quest about?

#### Entropia

well. i guess i made myself unclear.

what i meant was.. everytime i think i have "found every single website on the net possible on a particular subject", it never ceases to amaze me some cool stuff that i do miss, and only know about it when i actually *ask* people if they know of any particualr sites.

This is probably all stuff you know but the most basic rule is just the geometric principle that the angle of incidence will equal the angle of reflection. So if the ball hits the side of the table at an angle of 25 degrees, it will rebound at that angle. If a ball hits another ball, the angle that it bounces off at will be similar to the ball bouncing off a wall tangential to the surface of the (struck) ball. When you hit the cue ball, the momentum from the stick is transferred to the cue. The cue transfers part of its momentum to whatever it hits. The total momentum is conserved, so that knowing the initial conditions should lead you to predict the outcome with vector analysis.

#### Alexander

Don't also forget rolling friction (with k~0.05 for typical pool) which also applies to collisions with walls.

#### Artman

This is probably all stuff you know but the most basic rule is just the geometric principle that the angle of incidence will equal the angle of reflection. So if the ball hits the side of the table at an angle of 25 degrees, it will rebound at that angle. If a ball hits another ball, the angle that it bounces off at will be similar to the ball bouncing off a wall tangential to the surface of the (struck) ball. When you hit the cue ball, the momentum from the stick is transferred to the cue. The cue transfers part of its momentum to whatever it hits. The total momentum is conserved, so that knowing the initial conditions should lead you to predict the outcome with vector analysis.
The problem with this is that the effects of english (spin placed placed on the cue ball when hit) changes the geometry, effecting the cue ball bouncing off a cushion, draw, etc. and just generally make a mess of the geometry.

#### Alexander

Yes, adding rotations and sliding friction essentially comlplicates it. But still solvable.

That's true huh, I wonder if you can get some exponential curving. I've noticed that if I move the stick a shorter distance before it strikes the cue the cue bounces back less after it hits a ball. Lower momentum gives you less friction.

#### J-Man

I've noticed that if I move the stick a shorter distance before it strikes the cue the cue bounces back less after it hits a ball. Lower momentum gives you less friction.
I don't think the distance that the cue-stick travels is a factor. Perhaps you are only hitting the ball softer, or closer to center when this happens.
Also, doesn't the friction remain fairly constant? F=uN. It only matters if the ball(s) are at rest (w.r.t. the table) or moving, when u (coefficient of friction between balls and felt) changes. The velocity (hence momentum) is irrelevent for friction as long as it is > 0.

#### alleygl

Check these links out, Amateur Physics for the Amateur Pool Player by Ron Shepard (pdf file).
http://www.physics.ohio-state.edu/~penningt/262/ps/apapp.pdf [Broken]
http://www.physics.ohio-state.edu/~penningt/262/ps/apapp.pdf [Broken]
http://www.jimloy.com/billiard/phys.htm [Broken]http://www.jimloy.com/billiard/phys.htm [Broken]

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