The Physics of Colliding Balls

[vha3]

https://vanhunteradams.com/Pico/Galton/Collisions.html

[sebtron]

If you are interested in this topic, the author of pooltool[1], a billiards simulator, has a nice blog series about it [2].

[1] https://github.com/ekiefl/pooltool

[2] https://ekiefl.github.io/projects/pooltool/

[kazinator → sebtron]

This material deals with spin, unlike the article.

[ginko → kazinator]

It also has illustrations, unlike the article.

[amelius → sebtron]

And here is a video of a robot playing pool:

https://www.youtube.com/watch?v=dS6k0fcniH0

[angry_moose]

Also see the (somewhat legendary) "Perfectly centered break of a perfectly aligned pool ball rack" answer:

https://mathoverflow.net/a/156407

(updated link to original, not the repost)

[IanKerr]

For an interesting exploration of how even the simple physics of two blocks hitting one another can lead to surprising conclusions, I'd highly recommend this 3Blue1Brown video called "Why do colliding blocks compute pi?": https://www.youtube.com/watch?v=jsYwFizhncE

[phkahler → IanKerr]

>> Why do colliding blocks compute pi?

A lot of times with math I don't think the word "why" should be used. Those blocks computing pi was a good example where they "proved that they compute pi", but not really why. What is the real distinction I'm trying to make here and how to explain it?

[MiscCompFacts → phkahler]

There is no “why”, there just “is”.

[chkas]

I have programmed a small simulation of colliding balls in 2D.

https://easylang.online/show/#cod=jVPbbptAEH3frzhSpMqJFYppI0...

[pontifier]

It took me quite a while to understand exactly what was happening with a Newtons Cradle toy. You know the one with the clacky balls that swing...

If you hold 2 balls up, and let them fall, 2 balls swing up on the other side. How does it know how many you swung??? It boggled my mind for the longest time. Then I got to playing with one, and found something interesting. It doesn't always seem to work!

If the balls are perfectly aligned, and touching each other, the effect is dampened by the multi-body collision. It's strongest when the balls are just barely not touching.

What we see as multiple balls swinging and hitting is really a whole bunch of individual 2 body collisions that are close enough in time to seem like they are a single event.

I could be wrong about the reason, but this was my observation.

[TheRealPomax]

While rare events, it would be lovely if this also included notes on how to deal with "more than two balls" simultaneous contact cases.

[amai]

Classical mechanics is easy. Make the same calculations using relativistic mechanics for some real fun.

[kookamamie]

A very nice article. I noticed a small typo: "resitution".

[kazinator]

Unfortunately, this writeup doesn't mention any words like "spin" or "rotation" or "angular", not even to disclaim that those aspects are not presently being addressed. It looks like a great resource for kids in grade 11 or 12 physics.

[_Microft → kazinator]

The intended audience is the author himself.

Edit: You’re reading his notes/summary of the topic. Basically what he’s understood so far. “Expository webpages - For my own future reference. Intended audience is myself.”, see https://vanhunteradams.com/#Expository-webpages

[playingalong → _Microft]

Chances are the author is in 11th or 12th grade. And you two might be on the same page.

(Just joking).

[contravariant → kazinator]

Since it also doesn't mention friction I'm a bit confused what effect, if any, you were expecting to see.

Dealing with friction complicates matters significantly. At the very least you can't expect the collision to be elastic.

[kazinator → contravariant]

Actually, I believe that it can be elastic, if the friction is so great that the surfaces do not slip the entire time they are in contact.

[Jerrrrrrry → kazinator]

til how rubber bouncy balls work

[kazinator → Jerrrrrrry]

Yes. They can bounce back and forth due to the spin reversing. I believe each time they make contact with the floor, high friction causes of spent to stop, while they undergo a rotational deformation, which then reverses direction.

[anthk]

Koules was cool.