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Science

Physics of Billiards 82

Chris May writes "Amateur Physics for the Amateur Pool Player seems to have been around a while, but I have never seen it mentioned here. I know it would appeal to much of the Slashdot community-- 109 pages of complex Newtonian mechanics, on a trivial but informative subject. Hard to believe someone went to all this trouble." I'm having painful flashbacks - must - suppress - memories.
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Physics of Billiards

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  • What about the fact that Newtonian Mechanics don't work in the real world?

    I mean, I'm not that good at pool, but in the future I want to be able to break *really* fast. :)
    ---
    pb Reply or e-mail; don't vaguely moderate [ncsu.edu].
  • Tut via Newtonian Physics est aperteni al nia!!
    --
  • by Anonymous Coward on Saturday February 24, 2001 @12:05AM (#406305)
    Don't base any big money winning shots on these equations. These only hold true until .1c or so -- then they kinda start to fall apart.
  • by qpt ( 319020 )
    At Sourceforge [sourceforge.org] I am beginning an open source pool simulation project, and this information is exactly what I was needing.

    I had already spent a few days at a pool table making measurments with a ruler to figure out the physics of pool, but this will save me years of work. The project, by the way, is called X-Pool [sourceforge.net] and I am very interested in recruiting developers.

    - qpt
  • Don't base any big money winning shots on these equations. These only hold true until .1c or so -- then they kinda start to fall apart.

    Damn, and here I thought my relativistic linear accelerator pool cue was gonna revolutionize the game. Guess I'll have to crank it down to some paltry hypersonic speed...

    --

  • Newton's mechanics DO work in the real world!!! This is an all-too-common misconception. They only break down at speeds close to that of light. (In which case Einstein's laws apply.) I don't think you'll be breaking a rack at a speed near 186,000 miles/sec anytime soon! :P

  • by XO ( 250276 )
    Of course, the book, like all other books on billiards/pool, does not actually discuss -real- physics with pool. You'll never find a perfect table or a perfect cue unless you own them both, and take excellent care of them.
    Imagine sitting in a pool hall, drinking some brew, smoking a stogie, with your nose in this book between each shot, studying the exact way to hit it, and being perfect, except instead you miss every damn thing on the table because the cue is warped, and the table leans. :-)
  • by Anonymous Coward
    i dont know about you, but i am just happy to play with my balls [slackersguild.com]
  • I don't know beans about physics, but I can tell you that the shot on the home page will probably put "follow" (sometimes referred to as "forward English") on the cue ball, as long as the player has a good stroke and a properly-shaped and well-chalked tip. This ball will tend to roll forward of the natural line after it makes contact with the object ball.

    All your racks are belong to us !!

  • Not neccassarily as some of the most skilled billiards' players get paid the big bucks. Although while I must say I am not "skilled" at pool, I am fairly adequate and can hold my own, most of the time. ;)
  • Absolutely, one should rather spend time dilegently sharpening one's skills at the gentlemen's game of Quake III Arena. Clearly.

  • For example, where are the formulas for deformation of the playing surface due to the 350 pound man who leans his stomach onto the table to make the distance shots?
  • by Shoeboy ( 16224 ) on Saturday February 24, 2001 @12:30AM (#406315) Homepage
    Slashdot editors are constantly making references to the math, science and especially computer science courses they took in college. I have yet to hear a single one wax nostalgic about an English or creative writing class.

    Why is this?

    --Shoeboy
  • This piece should be titled, "Amateur Physics for the Amateur Pool Player Who Is An Engineering Major In His Spare Time". The Introduction was promising, but page 1 has a big nasty equation right in the middle of the page! Quickly leafing through the rest of the document, I found not a single page without radicals, sigmas, or integrals, and indeed several pages had nothing but! In conclusion, the reading of this document should be avoided in the same manner one would avoid the reading of the source code to X.
  • by Ukab the Great ( 87152 ) on Saturday February 24, 2001 @12:35AM (#406317)
    I wonder if we'll eventually see a computer/robot vs. Human pool match a la Gary Kasparaov & Deep Blue? A pool playing robot would be simple enough (in comparison to something like Deep Blue) that any big engineering college should be able to put one together. Put it up against a world champion pool players, and you've definately got something for pay-per-view.
  • But the way my pals and I were playing last night, we damn near managed it!

    Unless the document's got handy advice for factoring in the effect of alcohol on shot selection, then sadly it will be wasted on me!

  • by Anonymous Coward
    Neat game!

    I finally found a link [sunsite.org.uk] to it.
  • by Calle Ballz ( 238584 ) on Saturday February 24, 2001 @12:57AM (#406320) Homepage
    ....these physics actually apply during tournaments. I think that during actual competition, everything reverses itself, all laws of physics go wacky, and a magic invisible goblin sits in each pocket and diverts all balls away from the pockets.

  • What you say!!

    --
  • by xkenny13 ( 309849 ) on Saturday February 24, 2001 @01:08AM (#406322) Homepage
    Er wait ... doesn't somebody have a patent on this?
  • Yeah, do they take into account what happens when you propel the ball at relativistic speeds?

    I thought not.
    --
  • by nomadic ( 141991 ) <nomadicworldNO@SPAMgmail.com> on Saturday February 24, 2001 @01:19AM (#406324) Homepage
    I assumed by the spelling in their posts that they never took those classes...

    Sorry, I know it's mean, but I couldn't help myself.
    --
  • Actually, I intended for the above post to be a joke. Back to the drawing board for me :(
  • More correctly, Einstein's rules work in the real world. Newton's laws, which are based on his observations of many years ago, hold true in a particular subset of the real world, where nothing is traveling quickly relative (no pun intended) to the speed of light.

    Close, but no cigar. Newton's "laws" are an approximation of the truth. Einstein's theories are a better approximation. We don't know if a still better approximation will be developed in the future.

    Newtonian physics is a better approximation the farther speeds are restricted below light speed, but there is no cutoff. As long as things are moving at all, there is some relativity effect.
  • Oh, shut up you uneducated american boor. The quote belong's to Churchill and is in no way to be taken as "job advice."

    We were too busy learning the correct usage of "belongs" and that we should capitalize "American".
    --
  • by s390 ( 33540 ) on Saturday February 24, 2001 @01:40AM (#406328) Homepage
    Good for you and your pals!

    Have you ever played pool (or billiards, a rather different game) for drinks or money? I have done that, with about even success (you win some, then you lose some, it all works out just about even). But getting _really_ good at it takes real focus. I've seen a very good player. It was impressive. A good player can run 150 balls, straight pool, without a miss, and make it look easy. That's good! Sort of like programming skills... There's a ten or more multiplier between patzer and master, in terms of effectiveness.

    On a good night, I can hold a pool table against all comers. If drinks are bet, I drink for free, in the US, Middle East, and Austrailasia. But I'm not exceptionally good.

    My wife, however, used to take guys for real money at pool. Part of it was the way her skirt hiked, leaning over the table. But she was also skilled, and ruthless about it.

    A CIO I once worked for had previously made his living playing pool, for a while when between jobs. I did not seek out an opportunity to play poker with this individual....

  • Although while I must say I am not "skilled" at pool, I am fairly adequate and can hold my own, most of the time. ;)

    It's interesting, but pool is one of those few pursuits where nobody seems to want to admit to inadequacy. Even the most modest people seem to boast how much they "rock" at it. Who knows.

    Except me, btw. I'm really bad at it.
    --
  • All your base are belong to us.
  • Tut via bazo est aperteni al nia!!
    --
  • by Karma Sponge ( 319502 ) on Saturday February 24, 2001 @02:14AM (#406332)
    Let me tell you. Back in my college years I would carry this document with me wherever I went. To call it dog eared would be an insult to any dog. The corners were mangled, the text was blurred on many a page. Countless nights I spent visually caressing this wonderous text -- to the punishment of red eyes in the morning. I clearly remember nearly failing a 3rd year physics final exam because I had spent the last 3 nights studying the object ball throw sensitivity diagram on page 45 instead. Or how I would always give myself a chuckle by looking at the computer program I created to solve for the table of values required for problem 5.6.. Ahh, to be so young and clueless! Such unoptimized code! Regardless, I hope all of you can explore and hopefully enjoy this textbook of wonders. A text worth its weight in gold, if you were to print it onto an atom.
  • ...yet falls a bit short of the mayrad imprecise human endeavors that we all take for granted. In doubt? Spy the numerous comments as to the sufficiency of mankind. Oddly, and not unlike computer chess, this sort of mathematical modeling has been around since most of you Slashdotters were still playing with Cabbage Patch Dolls. (I don't mean that as a put-down, in any way, but merely as a historical reference.) Highly perceptive of the poster to point out that this has not been seen here before. The original Crays, Big Blues, and all of the other eccentric PARC, MIT and Cal (forgive ommissions!) "superconmputers" were after one thing back then: to be more human. Hence the birth of "Artificial Intelligence". (Whatever became of that supernatural phrase, I wonder?) Now we live in the world where database programmers using free-as-in-umbrellas software are doing things these "fuzzy logic" hacks of old were only dreaming about on cocktail napkins. (And I should know, I was one of them.) I swear to you all, and forgive the preaching, we live in the future. Not just the now but the future dreamed of by so, so many. Now is the time. Use it wisely. You have the tools.
  • Someone did this with snooker a while back (>15 years) in England. There was a spot on Tomorrow's World about it. They had a robot setup overhanging a half-size snooker table. The software looked like it was quite sophisticated - looking ahead in the break and taking account of error, but the robotics part wasn't very good. I seem to remember Steve Davis commentated a game between the machine and a famous snooker referee.

  • by Anonymous Coward on Saturday February 24, 2001 @02:50AM (#406335)
    I think that good pool players can not only calculate where the balls will go if they hit it a certain way, but they also solve the reverse problem:

    Where do I want the balls to be at the end of my shot, so that if I miss my opponent will have a hard time, and if I don't miss I will have an easy shot. How can I get the balls to such a position. And, better pool players probably look a couple of steps ahead: if I shoot here she might be able to shoot there and then there and then there.

    Anyway. Just calculating where the balls go if you hit them a certain way is a good start. But maybe it is a bit akin to knowing where a chess piece will get to if you move it a certain way?

  • by Restil ( 31903 ) on Saturday February 24, 2001 @03:50AM (#406336) Homepage
    During my freshman year in college I would always skip physics class to play pool. Somehow this seemed like a legitimate use of my physics time, since it was at least SOMEWHAT related to the subject matter. Sorta. Well, it was an adaquate excuse for MY purposes. :)

    In any event, had this manual been available, I might have actually thought to consult it, and I might have actually learned some physics during this time period, although I did get rather good at playing pool. :)

    -Restil
  • I have yet to hear a single one wax nostalgic about an English or creative writing class.

    I suspect it that like so many of our colonial cousins, they have lost touch with their cultural roots in England. I mean, the USA has butchered the English language (the language of Shakespeare, Milton, and the Bible) and has replaced it with a kind of 'McEnglish' where everyhing is spelled wrong (e.g. color instead of 'colour', tumor instead of 'tumour' etc) and new words are introduces where perfectly good ones already existed before (deplane, discomfortableize, etc etc).

    I blame the schools for not teaching about Americans where they originally came from (e.g. England) and concentrating too much on "political correctness". Fortunately you will not find too much of that in the UK ;-)

  • Actually, you've yet to hear a single one wax nostalgic about a math, science, or computer science course either. :)
  • Back in my college years
    ...
    computer program I created to solve for the table of values required for problem 5.6

    If you went to college at a time when computers were that available, it doesn't quite qualify as "back in the day" material just yet. And I am in fact ruling out that you wrote the program on punch cards, because given the condition of your pool physics book, I can just imagine the punch cards by the time you got 'em ready to run. ;-D
  • Are you kidding? Lack of skill at billiards is a sign of a wasted adolescence. What the hell did you do with your adolescence that was less wasteful than billiards? I'm not really good at pool or anything, but it's still one of the absolete best pastimes for the disgruntled student.
  • Just gimme that Math short from Disney with Donald Duck and I'll hustle all of ya!

    --Chemguru
  • by cunninglinguist ( 165101 ) on Saturday February 24, 2001 @05:24AM (#406342)
    function location() {
    if (my.state != "coding" & my.conscious == true)
    {

    return ("at the pool hall");

    }
    }
    and while at the pool hall (Amsterdam Billiard Club, NYC) I have watched and played many professional pool players.

    Yes, pool is governed by the laws of physics (even when your opponent snaps the nine-ball in three consecutive times).

    No, knowledge of these physical laws will not make you a professional player.


    Take a bank shot, for example. If you assume that the angle of deflection of the object ball into the rail equals the angle of deflection, calculate that angle and shoot, there's still a good chance you won't make the shot. One reason: from table to table the hardness of the rails varies.


    A few other variables which your ruler and protractor probably won't account for:


    crap in the air (humidity affects the speed of the cloth)
    crap stuck to the balls
    crap on the table (damn that shard of chalk!)
    crap on your cue tip (chalk/no chalk?)
    crap going on around you (people talking about the likelihood of you missing)
    crap on the line (the money you're about to give the guy who's kicking the crap out of you.)


    So, when you get right down to it:

    pool == physics + Random (crap);

    and the good players have a better sense of smell.



  • What about amateur physics for the naughty amateur?
  • Either that, or an American Pie-like love experience with the table (or, help us all, the cue).

    Then again, he might just be referring to some class about Newtonian mechanics (physics?), information which has since escaped his grey matter in lieu for more useful knowledge [slashdot.org].
  • Does anyone else remember the little Disney cartoon with Donald Duck that talked about the same thing? It was made in the 50's or 60's I think and I saw it in the mid-80's. My memory is a little foggy, but I think I remember them using some trig to explain the relationship between the taget pocket, the ball you want to hit, the cue ball and the little dots on the side of the table. It was pretty complex for a seven or eight year old, but I remember actually understanding it and testing my new found knowledge the next sunday at the arcade. Of course I can't remember very much of it now. Does anyone know the name of this?
  • "oooh, you English are soooo superior, aren't you!?" -Otto

    ---

  • >I mean, the USA has butchered the English anguage (the language of Shakespeare, Milton, and the Bible)

    You did know that the Bible was written in Hebrew and Greek, right? It was not written in King James English. Ahh, English, the language the Iliad was written in...
  • You are a wanker(was wanker Milton or Shakespeare?). The Bible was written in Hebrew and then poorly translated into English. Language is a dynamic thing. English in the UK is not the same as it was in the days of Shakespeare or Milton, so we 'Merikans are not the only ones to "butcher" the language.
  • You, sir, are a troll and a fool.

    Your pardon, but the last time I spoke with anyone in the UK, they sounded not a whit like any Shakespeare or Milton I've ever read. And what about Middle English? You think you could sit down and rap with Chaucer? Surely that's the 'true' English--which you are just as far from as us. And the Bible, of course, was hardly written originally in English. The English educational system is much more deficient than the American in many regards; for instance, it seems to have left you with the preposterous idea that Americans are all from England when this is in fact clearly not the case.

    I submit, sir, that your version of English is outmoded and has been superseded by a superior edition, as practiced here in the United States.

    Good day to you, sir.
  • Mirror anybody?
  • Who won in "Silent Running" on the Valley Forge? Bruce Dern or the "robot"? I haven't seen that movie in a long time but I recall a pool (some odd "futuristic" version) playing robot.
  • It looks like most of the posts so far claiming to have read it are really jokes. But if someone on Slashdot actually has read it, it would be great if they could review it on The Assayer [theassayer.org].


    The Assayer [theassayer.org] - free-information book reviews

  • It seems incredible to me the way you Americans are obsessed with sports and statistics. Over here in your Motherland (The UK) we think of sports as slightly humorous and a bit of a waste of time. We would never dream of paying a sportsperson the sort of amount that American sports stars are regularly awarded.

    In Her Majesty Queen Elizabeth IIs kingdom we measure a persons success by their class, breeding, and manners. None of which have anything to do with how fast they can run or how good they are at throwing a ball around.

    It strikes me that in the US, the lack of a proper class system leaves a vacuum which has been filled by mindless worship of sports, and to the cult of the 'Jock' as I believe you call people who are good at games.

    Anyway I am in danger of becoming offtopic. A site such as slashdot, catering as it does to the more thinking, educated sector of the American population should think carefully before posting 'sports' stories like this, no matter how interesting the physics may seem, it is a short step away from joining the mainstream of America, with its mindless sports obsession.

    Slashdot - please, I implore you, lets have no more of this sports nonsense, try and stick to 'news for nerds - stuff that matters'.

    Finally, one observation. Given most American's obsession with pornography in all forms (thankfully illegal here in the civilised UK) I would have thought they would be more interested in the 'physics of pocket billiards'

  • http://library.thinkquest.org/C006300/main.htm [thinkquest.org]

    /*
    *Not a Sermon, Just a Thought
    */
  • And in a system sensitive to minor changes, such as pool, do these relativity effects matter a shit at typical pool-speeds?

  • ... are as follows:

    1. The probability of the white ball dropping into a pocket ist at least three times as high as that of any other ball.
    2. The table's rails have an increased gravity. Balls tend to stop only so close to the rails that a successful next shot becomes almost impossible.
    3. The laws of reflection do NOT apply to rails on billard tables.
    4. If you try to pocket a ball and fear that the white ball will drop as well, then it will.
    5. If you change that shot so that the white should stay on the table, it will still drop.
    6. If you do try the shot but concentrate so much on not pocketing the white ball that you even miss pocketing the original ball, the white ball will still drop.
    7. The worst novice will succeed in making the most unbelievable and impossible shots.
    8. The same novice will at the same time manage to screw up a ball that actually was so close to a pocket that it didn't seem possible to not pocket it; instead, this ball will move away from the pocket and the white ball drops.
    9. Not caring about a shot and blindly shooting the white ball across the table will increase the likelihood of a positive outcome.
    10. 8 balls can not make it into the intended pocket, unless by a strange accident.

    OK, maybe that is a little inspired by Murphy's Law, but I've seen it happen. Really.

  • I have yet to hear a single one wax nostalgic about an English or creative writing class.

    And be nailed as an English Nerd?

    Oh, for goodness sake! Everybody knows that a Science Nerd can beat the crap out of an English Nerd.
  • oh, i'll easily chime in here.
    i own a table and am still bad.

    i understand the physics, i understand the intended means to execute that physics.

    i just can't make the two meet :)

    Peter
  • You've read _Practicle Demonkeeping_, huh?
  • NB:I am American. You claim that the values with which you define success are superior to our values. What makes your choices of values better than our choices? From what I see, they are fairly equal: you choose to measure success by "class, breeding, and manners", the first two which are assigned at birth. You claim that we measure success by the skill we have at "run or how good they are at throwing a ball around." Those, also, are somewhat determined at birth, less so admittedly than class or breeding, but you get the point: what you call value is determined at birth, as what you claim we value is also. (whether I agree that sports = value is another point, but I am merely discussing your post) I ask, then, what makes breeding and class better values than skill at running or throwing? You attack the values of our society (whether they are really our values or not) without providing any basis for your claim that yours are better than ours. In fact, I would go as far as to say that I would rather have athletic prowess as a measure of success than breeding or class. I would rather have a trait that requires some work to develop (though it depends somewhat on birth) than one that depends entierly on your birth and the merits of others! Even disregarding my opinion on the matter, the objective fact is that your opinion on the definition of success is flawed logically as your definition of success is based on grounds that have little difference from ours.
  • And you, Sir, have been trolled. fool.
  • obviously a true student of the game; well observed. Add:

    9. Acts of cat | God | insect will be of more benefit to your opponent thant you.

  • As I recal, it was called "Donald Duck in Math-Magic-Land" I think it only showed him how to "play the diamonds" and how that related back to simple geometry. I think Donald's way of winning came from the "if I hit the ball hard enough, it will eventually knock something in" school of billiards.
  • Yup yup...chess is the same way.

    "Chess, huh? I kind of suck, and I haven't played in months..........but I'll kick your butt any day"

  • Your first few words just inspired me to create a new acronym: IANAA (I am not an American) And quick, I'm patenting it so no one but me can use it! Or at least mention my name when they do. It will be my 15 minutes of fame!!! Hahaha. "Freak.."
  • The English and creative writing courses in America are taught by the kind of people who honor James Joyce. Which is like learning biology from a creationist, astronomy from a Ptolemaic, or chemistry from a man researching the Philosopher's Stone.
  • if the physics are easy enough, the computer will never miss, and it doesn't have to think about that sort of thing
  • What if you hit the ball at near light speed? It changes all the angles...
    --------
  • er, I don't equate replying to a troll with a tongue-in-cheek movie reference to YHBT

    what are _you_ talking about (...and no need to get personal)?

    ---

  • RECREATIONAL MATHMATICS tribute to Grey Havens...
  • kick your ass out of their country, liek we did.

    Ask any historian, and they will tell you that the defeat of the British in what is now the USA was entirely caused by political problems in England (your motherland).

  • by Wills ( 242929 ) on Saturday February 24, 2001 @04:30PM (#406372)

    The first robot ever to play snooker (related to the game of pool) was developed under a team led by Professor Khorosh Khodabandehloo at the University of Bristol [bris.ac.uk], UK.

    The Bristol snooker robot played a famous match against the then world snooker champion, Steve Davis of the UK. The robot, a customised IBM Model 7565, was severely handicapped because its operating envelope covered only about 87% of the table and also because freeplay in its joints limited its mechanical accuracy and repeatability. The strategy part of the robot was quite sophisticated having been based on advice from Steve Davis himself. It was able to make forward and reverse analyses of states of play based on support logic programming (related to but more powerful than fuzzy logic programming). The cue it used to hit a ball was actually a pneumatic piston powered by compressed air. Davis beat the robot easily! As an undergrad student, I helped to design, implement and test the robot's image processing software using the now defunct Automatix AV4 Image Processing System once made by Robotic Vision Systems, Inc. [rvsi.com].

    The whole project was filmed and shown on BBC television [bbc.co.uk] on the Q.E.D. science programme of 16th March 1988. Extraordinarily there are now no webpages at Bristol University to celebrate this pioneering robotics project. Professor Khorosh Khodabandehloo has left Bristol University to run his own robotics consultancy. One of his former research assistants, Ken Ho, however, has made webpages about the Bristol snooker robot: here [netscape.net] and here.

  • from the pocket-pool dept.

    I think the physics for that particular variant of the game can be found here [jackinworld.com].

    --
  • These physics questions are rather useless. As a pool player, I think the most important question that no one has explained clearly in physical terms is "How to draw a ball."

    I have talked to pros and semi-pros and read lots of books about drawing the ball on the pool table. Contradicting suggestions: lift the queue butt . don't lift the butt. And then, the one suggestion from professional player: just practice every shot as a draw until you get it.

    There is a certain "stroke" that is required to make a draw shot. no one can explain the "stroke."

    I don't like the idea that every newbie must go through the painful process of discovering the "stroke" of a draw. it would be interesting to see if any good physical explanation can help. For many years, I have wondered about it. Now that I know how to make a draw shot, I still cannot explain it.

    I talked to a physics PhD student about it. he seems to be contempt with my theory of the cue tip accelerating after the initial compact and get stuck on the cue for a little bit, but frankly i am not happy with this analysis.
  • "a trivial but informative subject."

    Trivial my ass! I play pool at work for at least an hour a day. Here in the Herndon/Reston Virginia area, tech job fairs are regularly held at the local pool halls. For us, pool is far from trivial.
  • but pool is one of those few pursuits where nobody seems to want to admit to inadequacy

    Not true. Pool is famous for people who claim inadequacy ... right before they offer to double the bet.

  • I believe that calling this a troll just proves my point!!!
  • The fun of pool physics.
    I decided to build my own pool table and learned quite a few things while tring to cut corners on cost.

    There are three major types of bummpers and they all play differently. There are a number of different sized balls that are made out of two common materials and a few not so common ones. Two balls if a different material will of course rebound differently depending on the spin. Different materials will also make changes on the spin. The cloth will always have differnt rolling frictions depending on the angle of the ball relative to the weave direction. The temperature of cloth will also effect the friction. The friction between the balls and cloth can often exceed hundreds of degrees.

    There used to be lots of useful info at: www.bestbilliard.com but I can't get there right now.
  • "It seems incredible to me the way you Americans are obsessed with sports and statistics. Over here in your Motherland (The UK) we think of sports as slightly humorous and a bit of a waste of time. We would never dream of paying a sportsperson the sort of amount that American sports stars are regularly awarded."

    No you would just murder their goal keeper if their team beat yours at football. You're so full of shit you can't see straight you dumb fucker. If brits don't care about sports why were you temporarily banned from football matches? Why are quotas still placed on brits limiting the # of them that can attend football matches? Because everyone knows you hooligans are too primitive to act like adults.
  • moron: pool and billiards are different. look it up
  • Newtonian mechanics works fine for pool balls, its only in the limits that things become very small (Quantum Mechanics) or very highly energetic (Special relativity) that it's not accurate any more
  • >Take a bank shot, for example. If you assume
    >that the angle of deflection of the object ball
    >into the rail equals the angle of deflection,
    >calculate that angle and shoot, there's still a
    >good chance you won't make the shot. One reason:
    >from table to table the hardness of the rails
    >varies.

    Even without the hardness of the rails coming into play, you'll probably miss if you only take into consideration the absolute angles anyway, and not for the reasons you mentioned later in your post.

    The speed of the shot will cause the angle to narrow.

    Take two shots at the same spot on the rail from the same spot on the table. Hit one softly and the other quite a bit harder. The ball you hit harder will rebound with a much narrower angle.

    -LjM

  • There are going to be narrow-minded, self-serving jerks in any profession, including IT. A well-rounded professional is one who keeps up to speed on his or her profession and makes an effort to stay informed on issues only tangentially related to the profession.

    I guess I don't understand why you feel that you had to leave physics just because the professor was a jerk, or why you think that the IT industry would be any different.

    I happened to thoroughly enjoy my humanities classes during college, and had more than a few obtuse science professors, yet I did not choose to change my major or drop out because of that.

    In a desparate attempt to get back on topic, I will say that anybody familiar with physics would know that plugging numbers into the billiard equations will not result in exact predictions of the real world. Even more "accurate" equations taking quantum mechanics and relativity into account would fail after a few collisions. Your prominent scientist must have been incredibly toasted if he was claiming that any particular set of equations were "true"

  • Or what about those things we used to refer to as 'gravity wells' on the surface of the pooltable in the dorm basement (we're not talking little dents here, we're talking 2cm+ dips in the table -- I got real good at playing the ball off them, though, much to my humanities-major friends' annoyance)

Friction is a drag.

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