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Pancake Physics to Cut Batter Splatter 313

Posted by chrisd
from the all-hail-science dept.
Anonymous Coward writes "The headline just about says it all on this one. A physics grad student in the UK has come up with the mathematical formula for how to flip a pancake and have it land correctly back in the pan. The BBC has the details."
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Pancake Physics to Cut Batter Splatter

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  • Ah-hah! (Score:4, Funny)

    by Gortbusters.org (637314) on Thursday March 06, 2003 @04:02AM (#5447704) Homepage Journal
    His secret is revealed: The angular velocity of the object equals the square root of Pi, times the gravity divided by the distance the pancake is from the elbow times four - that is how to get the pancake back in the pan.

    Seriously, mimicing real life movement in mathematical forumla is a tough one (that's why we don't see any battlemechs [classicbattletech.com] walking around, or tons of popular robots in every house hold.
    • Re:Ah-hah! (Score:2, Funny)

      by Zenjive (247697)
      The angular velocity of the object equals the square root of Pi, times the gravity divided by the distance the pancake is from the elbow times four - that is how to get the pancake back in the pan.

      Would that be an African or European swallow?
    • For something this (relatively) simply, it works pretty well. It's not like you have to worry about wind drag or something.

      Since I have year-old twins that are just starting to eat pancakes, this will come in handy!

  • by marnanel (98063) <slashdot@@@marnanel...org> on Thursday March 06, 2003 @04:05AM (#5447709) Homepage Journal
    Americans should bear in mind that what are called "pancakes" in England are called "crepes" in America. What are called "pancakes" in America are called "Scotch pancakes" in the south of England, and "drop scones" in Scotland and the north of England. Meanwhile, "flapjacks" are a kind of oaty biscuit. Confused yet?
    • by Xxanmorph (654953) on Thursday March 06, 2003 @04:39AM (#5447826)
      Too much information about other countries! My american brain can't take it!
    • Having been in London recently, and yearning for American pancakes, I had no problem finding many restaurants offering American pancakes and calling them... guess what... "pancakes". Looks like we're rewriting English once again.
    • Americans should bear in mind that in Canada they're called "Back cakes" also...
      "... equals the square root of Pi, times the gravity divided by the distance the pancake is from the elbow times four ...
      You'll have to double that and add 30.
    • Confused yet?

      Actually, what I found more "confusing" was the bit at the end of the article about more Britons preferring lemon and sugar on their pancakes... Bleh. :)

      Incidentally, I'm from New England, where a milkshake is only a milkshake if it has no ice cream in it, otherwise it's a frappe (unless you're in Rhode Island, where it's a cabinet), unless the ice cream is not blended, in which case it's a float.

      -T

      • When I was 6 (many many many moons ago), we lived in Boston for a year. I still remember my sister ordering a chocolate milkshake, and getting...

        Chocolate milk shaken up (not stirred :-P)... She then found out she had wanted a "frappe".
      • Damn Yankees and your corrupt food terminology with "pop" in your "floats" and no ice cream in your shakes. It must be another liberal conspiracy. Now, where did I put my Big Red and Moon Pie.
    • Down here in Australia, US:Crepe = AUS:pancake, and US:pancake = AUS:pikelet. I believe there are parts of England where this is also the case.

      Russ %-)
  • by Boss, Pointy Haired (537010) on Thursday March 06, 2003 @04:05AM (#5447711)
    It will make sure the pancake will land back in the pan, as long as you understand the formula.

    Understanding something does not equate to being able to do it.

    I understand how a plane flies, but I can't fly one.
    • by ender81b (520454) <billdNO@SPAMinebraska.com> on Thursday March 06, 2003 @04:19AM (#5447765) Homepage Journal
      Heh. I'm a line cook here in the US and there is quite a bit more to flipping American Pancakes (I realize english pancakes are somewhat different).

      Stuff like how long you wait till you flip it, the perfect angle to get the spatula underneath the pancake (directly parallel to both the grill and the pancake), what to do with blueberry/raspberry/banana/etc pancakes, what to do when the cake sticks, and the rest. I'm sure you could come up with an equation to perfectly predict this and it wouldn't mean a damm thing -- like this one.

      I mean you could equally use a formula to try and tell somebody how to flip eggs and it wouldn't meen a damm thing. To train line cooks to flip the proper, and perfect, Over Easy egg requires about 100-200 wasted eggs until you get it down to about 95% of the time -- and that extra 5% is a pain since each egg varies in how much force will require before it breaks, etc and usually requires thousands of eggs before you can go nearly an entire 8 hour shift without breaking at least 1 yolk open. By 'flip' an egg I mean using only your wrist, no sissy spatulas involved. It takes alot of work and effort to learn to do these things which is why almost nobody outside cooks can probably cook eggs or omeletes the *right way*, no spatulas/informercial specials involved.
      • but why is it important to flip it in the air?
        • For eggs it is necassary to cook them on both sides obviously. Also, those little gimmicks won't work for line cooks because you can flip them in the air faster than anything with a spatula or other method and also because they don't necassarily work all the time.

          Basically for time saving. When you are cooking 20 eggs/omelettes at a time you have to be able to flip them in about 2-3 seconds, not waste a minute or more gently flipping them over/using some other method.
      • by Amroarer (645110) on Thursday March 06, 2003 @05:35AM (#5447932) Journal
        Well, where I come from, we don't use no spatulas to toss pancakes... (Although some more cautious people do slip them out of the pan onto a plate, then drop them back in upside down.) English pancakes are so wide and thin that a spatula's likely to just tear them. Instead you have to use the showing-off-method.

        First you make a circular movement with the pan to ensure that the pancake hasn't stuck and overcome static friction.

        Then you tilt the end of the pan down slightly and make a short, sharp inward movement, to get the pancake sliding outwards.

        Then you sharply flick the pan up, so that the pancake goes between one and two feet in the air (more if you're feeling cocky) and also spins enough that it lands in the pan the other way up.

        I'll be very impressed if they invent a machine which can repeatably toss pancakes. There are an awful lot of variables, which he seems to ignore. But then he is a physicist, not an engineer. ;-)
        • by WolfWithoutAClause (162946) on Thursday March 06, 2003 @08:56AM (#5448469) Homepage
          I'll be very impressed if they invent a machine which can repeatably toss pancakes. There are an awful lot of variables, which he seems to ignore. But then he is a physicist, not an engineer. ;-)

          Yeah, but that means he will be more accurate by roughly 5% because he won't be assuming that pi is 'nearly' 3 ;-)

        • - First you make a circular movement [...]
          - Then you tilt the end of the pan down slightly
          - and make a short, sharp inward movement [...]
          - Then you sharply flick the pan up
          - so that the pancake goes between one and two feet in the air [...]


          Thank you, both for the pointers and an approximation of what they formula should be rearranged to give.

          The formula expressed in the article purports to give you the angular velocity of the pancake. Perhaps useful as one step in the process of computing how to build a flipping machine, but NOT the whole story even for a machine design, and definitely not what you need for training a human.

          And the formula is clearly wrong, since g shouldn't be in it if you're going for angular velocity - unless you're solving for the angular velocity needed at launch to get the pancake back into the pan (in which case r shouldn't be there). So something in the article's description is wrong (though perhaps the original research was correct).

          What I'd like to see is a function giving the target height for the top of the pancake's arc in terms of the radius from pivot point (probably elbow) to the center of the pancake (and possibly also parameters for the mass and diameter of the pancake if air resistance is significant.

          It's a lot easier to target a particular height-of-toss than some other control parameter (such as speed), and the height will vary with the individual flipper's arm-plus-pan length.

          Since the pancake has to land back in the pan the toss has to be close to straight up, which puts the pan about horizontal at launch. There will be some small inward motion from the air resistance, because the up and down trip have the 'cake at opposite angles to the wind, which might be compensated for by outward motion from sliding on the pan during the angular swing of the launch.
          • And the formula is clearly wrong, since g shouldn't be in it if you're going for angular velocity - unless you're solving for the angular velocity needed at launch to get the pancake back into the pan (in which case r shouldn't be there).

            Oops. I take that back.

            g, r and omega should all be there to let you solve for time-of-flight from angular velocity. So rearranging should let us solve first for circumferential velocity, then for flight time, and finally for height-of-throw, giving the formulation I was after.
    • by arvindn (542080) on Thursday March 06, 2003 @04:22AM (#5447774) Homepage Journal
      You are mistaken.

      http://catb.org/esr/jargon/html/Some-AI-Koans.html [catb.org]:

      A novice was trying to fix a broken Lisp machine by turning the power off and on.

      Knight, seeing what the student was doing, spoke sternly: "You cannot fix a machine by just power-cycling it with no understanding of what is going wrong."

      Knight turned the machine off and on.

      The machine worked.

      In the same way, the pancake will land back in the pan as long as you understand the formula.

      [[Mods, mods: this is supposed to be _funny_. Its not the first time I've posted something hilarious and it got modded "Insightful"]].

    • I understand how a plane flies, but I can't fly one.

      You pull back it goes up. You push forward it goes down. Left is left and right is right. What more do you need to know? Hey! You're a pilot!

      We'll see who catches that movie reference.
  • Sounds good (Score:5, Interesting)

    by trotski (592530) on Thursday March 06, 2003 @04:07AM (#5447718)
    But since most of us geeks are pretty inept when it comes to anything physical, I still think my pancakes gonna land on the floor, no matter what formulas I apply.

    Now if we could only have some kind of a pancake flipping robot.....
    • Re:Sounds good (Score:2, Interesting)

      by revmoo (652952)

      Now if we could only have some kind of a pancake flipping robot.....

      Yes, leave it to geeks to spend thousands of dollars, and countless man-hours developing a machine to flip a pancake over.


      • >> Now if we could only have some kind of a pancake flipping robot.....
        >
        > Yes, leave it to geeks to spend thousands of dollars, and countless man-hours developing a machine to flip a pancake over.
        >
        > [.sig] Too much of a good thing is an awesome thing, but too much of an awesome thing is really really stupid.

        And even more of an awesome thing than that ...is a surefire way to get your web site with a pancake-flipping robot slashdotted!

    • The CMU Robotics club [roboticsclub.org] actually has a project to make a pancake flipping robot :)
  • by djupedal (584558) on Thursday March 06, 2003 @04:08AM (#5447724)
    "A pancake in the UK has come up with the mathematical formula for how to flip a physics grad student and have him land correctly back in the pan. The BBC has the details."
  • Butter! (Score:4, Funny)

    by Anonymous Coward on Thursday March 06, 2003 @04:10AM (#5447733)
    If you butter both sides, will it land on its edge?

    A better question, what if you butter the edge as well?
    • A better question, what if you butter the edge as well? It spins indefinately? Seriously, butter some bread and attach it to a cat, then throw it up in the air. Cats always land on their feet, but bread always lands butter side down, so the cat/bread combination will spin round and round indefinately. Have you ever been inside a power plant?
      • Re:Butter! (Score:5, Funny)

        by Ashtead (654610) on Thursday March 06, 2003 @04:54AM (#5447857) Journal
        Actually, the study of bread falling off table was taking into account the starting position which is on the table and with the buttered side up. Seems the height of the table and the inertial torque of the bread conspire to make it roll somewhere between 1/4 and 3/4 turns, and therefore fall face down more often than not. With subsequent need for cleanup. If the table had been about twice as tall as a standard table (60 in instead of 30 in) the pieces of bread would have time to tumble one full turn and thus fall face up.

        Falling cats are famously able to turn around and land on their feet. Unless the height of the fall is too large, the cat has no problems with that. I forgot the exact conditions of falling cats, but they are able to turn around in a fall in a lot less than the 30 inches down from a table.

        If the two were to be combined and the cat has a piece of bread strapped to it, it is the cat that prevails, being more active, heavier, and having a larger moment of inertia.

        I'd imagine that the same would apply to pancakes, and I have disregarded the risk of the cat eating the food.

  • by WebfishUK (249858) on Thursday March 06, 2003 @04:10AM (#5447734)


    Not sure about other countries but last Tuesday (4th) was Shrove Tuesday in the UK when we all make pancakes. For the religious amongst you the word 'Shrove' refers to the practice of confessing of sins, then afterwards the fast of Lent could be considered a penance of faults committed. Thats why the BBC ran the story on Tuesday. However, most of us just love eating the pancakes!

    • Shrove Tuesday is the day before Ash Wednesday, the start of Lent, the period of 40 days leading upto Easter where people would originally go without eating various dairy products for that period. History was that people would use up all the eggs, and milk in the house, so someone came upon the idea of making pancakes.

      I made some cracking pancakes on Tuesday, my special recipe involves grating bits of lemon and lime rind into the batter, mmmmm, that citrus flavour flows all through the pancakes, nice.

      I am not religious but it is always useful to know about as many different religions as possible as this gives you many excuses to feast, well that and setting off lots of fireworks.

    • Not sure about other countries but last Tuesday (4th) was Shrove Tuesday in the UK when we all make pancakes. For the religious amongst you the word 'Shrove' refers to the practice of confessing of sins, then afterwards the fast of Lent could be considered a penance of faults committed. Thats why the BBC ran the story on Tuesday. However, most of us just love eating the pancakes!

      Here in America, we call it "Fat Tuesday" (fitting considering the extra weight most Americans carry isn't it? ;) )

      I'm from Detroit, and we have a large Polish population here (according to one statistic, Hamtramck has the largest population density of Polish people outside of Warsaw) and so here we have the old tradition of eating paczkis, which are pastries of Polish origin not entirely unlike a jelly donut (but don't *them* that, it's SACRILEGE to compare a paczki to a jelly donut). The paczki is one of my greatest personal weaknesses. :)

    • Not sure about other countries but last Tuesday (4th) was Shrove Tuesday in the UK when we all make pancakes.

      Heh. In a large chunk of Catholic-dominated societies last Tuesday was Fat Tuesday / Mardi Gras / Carnival, celebrated by:

      Drinking copious amounts of alcohol
      Watching nubile young women disrobe
      Dancing in the streets
      Throwing / catching small trinkets (such as strings of beads) for good luck

      You Brits need to get with it!

      I've had the good fun of being on a float in one of St. Louis' Mardi Gras parades for several years now. This year my wife was queen of the float (yes, she found the baby in the king cake). So guess who got to ride up front with her? I'm still hoarse! :^)
  • Well, that's flippin' useless!
  • by psyki (653079) on Thursday March 06, 2003 @04:12AM (#5447741) Homepage
    The pancake problem has already been solved... What, haven't you seen the infomercial for the Pancake Pro? [tvadvertisedproducts.com]


    Make Perfect Pancakes every time! Now you can create mouth-watering pancakes that cook in an instant in this special two-sided pan. Just pour in your favorite batter, close, cook and flip--no spatula needed!
  • by _RidG_ (603552) on Thursday March 06, 2003 @04:15AM (#5447750)
    Dozens of TV cooking-show personalities weep in rage as this brave student unravels the greatest mystery of all time, thereby rendering their shows wholly irrelevant and useless. Emeril personally promises to track down this kid and "kick his balls up a notch." Stay tuned to Fox News as this story continues to develop.

    *flashy logo jumps onto the screen*

    "PANCAKE CRISIS: WHEN THERE IS NOTHING ELSE TO TALK ABOUT AT 1:12 AM!"

    *The camera cuts back to the weird-looking anchor Fox News always has. He smiles reassuringly, and gives you the thumbs up, proudly exclaiming, "This is Fox News! We are covering all the stories other news stations are too smart to cover!"*

    Extra points if anyone can spot the Onion reference :)

  • There is a serious game (with tournaments and all) which is somewhat similar to this. It's called tiddlywinks [cam.ac.uk]
  • by Boss, Pointy Haired (537010) on Thursday March 06, 2003 @04:16AM (#5447754)
    So no problem for most geeks then...
  • Is that.... (Score:3, Funny)

    by Highwayman (68808) on Thursday March 06, 2003 @04:18AM (#5447760)
    Is that Hans Blix in the article's photo? I long have expected the UK to be in possession of a proscribed pancake making machine able of launching a pancake in excess of 150km. In other news, Rumsfeld demands accounting for 1.5 tons of missing pancake batter.
  • by panurge (573432) on Thursday March 06, 2003 @04:20AM (#5447768)
    The BBC quotes a garbled version of the equation (haven't they got an equation setter? cheapskates) but clearly don't understand what it means.

    AFAIUI it simply means that the pancake needs to spin at such a rate that it will flip 180 degrees between leaving the pan and returning. Given that it will not fall back flat unless the flip is 180n degrees, n integral, this is pretty blindingly obvious.

    Unfortunately, the equation is just that and doesn't tell you how to achieve flip rate nirvana. So here is my guide:

    • First, use a nonstick pan with a gently sloping edge.
    • Second, use just enough oil to ensure the crepe can slide around smoothly.
    • Third, in order to flip, start by lowering the far edge of the pan so the crepe starts to slide towards the edge.
    • Then, as the crepe reaches the edge, rotate the elbow upwards so that the crepe slides off the edge in an upward direction. This provides the spin. The speed doesn't need to be too high. As the crepe flips over, catch it with the pan horizontal.
    • Start with small crepes and build up.
    • When I was first shown this technique in a creperie in Normandy, by the end of the evening I could flip them up to ceiling height and still recover them.
    Creperies that use precooked crepes made on industrial conveyor belts are of course beyond the pale.
    • by Anonymous Coward
      Given that it will not fall back flat unless the flip is 180n degrees, n integral, this is pretty blindingly obvious.

      ... I would further suggest that n is odd, or your guests will probably not be asking for a second round.
    • When I was first shown this technique in a creperie in Normandy, by the end of the evening I could flip them up to ceiling height and still recover them occasionally.

      Minor correction. :)

      -Thomas

  • A physics grad student in the UK has come up with the mathematical formula ...... The BBC has the details."

    Sure, knowing the formula is exactly the same things as being able to do is, but didn't anyone else notice that they didn't actually give this "formula" that they claim is so important?

    • umm yes they did. just wasn't written in matheamatical notation...

      "The angular velocity of the object equals the square root of Pi, times the gravity divided by the distance the pancake is from the elbow times four - that is how to get the pancake back in the pan. " and...
      "The 21-year-old explained the formula: "'W' is the angular velocity of the pancake, 'g' represents gravity and 'r' is the distance from the pivot - the elbow - to the centre of the pancake"

      so w=sqrt(pi)g/4r

  • MIT did it first ... (Score:2, Informative)

    by droopycom (470921)
    ...although less spectacular

    http://web.mit.edu/newsoffice/nr/1995/40409.html
  • re: story (Score:2, Funny)

    by prell (584580)
    if I ever get another story rejected by slashdot, I'll shoot myself
  • err (Score:5, Interesting)

    by Geaty (654469) on Thursday March 06, 2003 @05:22AM (#5447917)
    The angular velocity of the object equals the square root of Pi, times the gravity divided by the distance the pancake is from the elbow times four

    hmm . . . I notice that this formula does not factor in mass of the pancake. this makes me wonder, being not-so-smart in physics, would this formula apply for any size pancake?? and how about objects other than pancakes? could I flip say, a thanksgiving turkey and still have it land perfectly in the pan, using this formula??

    and why do Scots like cheese in their pancakes?? don't they know the proper way to do anything is the American way, i.e. sugar and syrup??

    Bored and tired minds want to know!!

    • Re:err (Score:2, Interesting)

      by theperplepigg (599224)
      Odd, I thought the american way was butter and syrup? Regardless, I'm american, and while I once loved syrup on my pancakes, I now prefer just plain butter/margarine (syrup occasionally, of course). Don't think I ever used sugar and syrup, though. Just seems like overkill to me.

      --paul

    • Re:err (Score:4, Informative)

      by gilroy (155262) on Thursday March 06, 2003 @06:45AM (#5448070) Homepage Journal
      Blockquoth the poster:

      hmm . . . I notice that this formula does not factor in mass of the pancake. this makes me wonder, being not-so-smart in physics, would this formula apply for any size pancake??

      In problems driven solely by gravity, the mass typically drops out. Thank you, Equivalence Principle.

      and how about objects other than pancakes? could I flip say, a thanksgiving turkey and still have it land perfectly in the pan, using this formula?

      A pancake is a nicely simple and symmetric object. Indeed, the symmetry means that whenever you flip it, you're doing so about a stable axis. Other shapes, not so nice... your turkey might tumble wildly. Also, while the mass drops out of the angular velocity, it does not drop out of the formula for the needed force -- and a turkey tends to be quite a bit more massive than a crepe.
      • the mass drops out of the angular velocity

        Mass only drops out in a vacuum. In air, while the pancake is aloft, you have

        angular acceleration = torque / moment of inertia
        Torque comes from air resistance and can be quite significant for a pancake weighing a few grams with a surface area of about 300 square centimeters.
    • Do you remember learning about something a bloke called Galileo did at the tower of Pisa? He didn't really do it, but if he did it would have been relevant to your question.

      Try dropping a pancake (crpe to Yanks) and and a melon at the same time. Which one hit the floor first? Oops. try it in a vacuum next time.

      So if you are cooking in a vacuum, the formula applies equally well to pancakes, melons, and thanksgiving turkeys.

      If you are cooking at atmospheric pressure, you will have to correct for air resistance (quite significant for a pancake).

  • by Nemosoft Unv. (16776) on Thursday March 06, 2003 @05:45AM (#5447949)

    I asked a (native) British collegue about it, and this was his reply:

    Ahh the wonders of pancacke day or as the French call it Mardi Gras Fat tuesday. This is the day before the start of Lent (crazy Christian starvation festival, preparing mind and body for the Easter celebrations etc). Typically people used to use up all their fatty things on this day such as butter, eggs and lard [freeserve.co.uk] etc, coz it was not the done thing to be eating lard cakes when everybody else was eating celery.

    Thus the pancake tradition started. Of course, all the religous nonsense has largely disappeared but the pancakes remain in British Culture.

    As far as the tossing equation goes, thats just the work of a whacked out English ale swilling academics, and is an essential part of British inventiveness and ingenuity. (You can't make great discoveries all of the time)

    Hope that helps and thank you for your interest in Britain.

    :-)

    • So let me get this straight -- while the US Gulf Coast from Mobile through New Orleans and west is celebrating the drunken debauchery of Mardi Gras, and while Rio de Janerio is celebrating the even more wild debauchery of Carnival ...the English are observing "let's eat pancakes day"? How dreadfully boring.

      No wonder our ancestors emigrated :-)

  • Okaaaaaay, (Score:5, Funny)

    by DongleFondle (655040) on Thursday March 06, 2003 @05:52AM (#5447974)
    I do believe it is time that someone introduced Europe to the concept of the 'spatula'. We sort a solved this whole pancakes on the floor dilehma a looooooooong time ago . . .
    You know what? While we're at it, let's give China forks and spoons.
    • by Inda (580031)
      Of course we have spatulas. How else do you think we scrape the ice off our cars on cold winter mornings?
    • But I'm not sure that we are convinced enough to make Spatula City [wayuhf.com] successfull in Europe.

      If you still think we should use spatulas, why don't you send a Virtual Spatula [virtualspatula.com] to prove your case.

    • You need to understand the difference between the US pancake ( CD-rom size only thicker) and the European crepe-type pancake (up to LP size, 30cm diameter, and beyond.) Even if you had a spatula large enough, you would struggle to get it under the crepe without tearing out the middle. Strange as it may seem, there is actually often reason and logic behind what foreigners do.
  • Off topic but... (Score:4, Informative)

    by the_pooh_experience (596177) on Thursday March 06, 2003 @06:01AM (#5447994)

    I know this is really off topic, but it is on, if the topic is "reasonibly absurd science". In Nature [nature.com] last December, they decided to publish a short note about an Austrailian matehmatician's work on The Best Way To Lace Your Shoelaces [nature.com]

    No joke.

  • BBC has something -- color commentary might be the best description. But to say that the linked BBC article has the details is just plain wrong.
  • by isa-kuruption (317695) <`ten.noitpuruk' `ta' `noitpuruk'> on Thursday March 06, 2003 @08:01AM (#5448255) Homepage
    There is something seriously wrong with the education system when a grad student gets a masters in physics for writing a thesis on flipping a pancake.

    What's next? Maybe, for his doctoral thesis, he should write a formula for the proper amount of syrup to be used based on it's rate of obsorbtion by the pancake.
    • What's next? Maybe, for his doctoral thesis, he should write a formula for the proper amount of syrup to be used based on it's rate of obsorbtion by the pancake.

      As long as he includes the effects of the butter on the pancake, I'd support that doctorate

  • we'll be reading a PhD* dissertation on the physics of flipping hamburgers.

    *piled higher and deeper

    ObJoke! "I'll bet you guys are excited" said the cabbie as he drove the students to their graduation ceremony. "I know I was when I got my PhD".

  • And they say art is dead, they obviously haven't seen what concerns physics grads are having to delve into to find something that hasn't be rehashed a million times.
  • by lonedfx (80583) on Thursday March 06, 2003 @10:17AM (#5448906)
    Pancake Algebra [pancakemath.org]

    not quite the same, but thoroughly enjoyable !

    Francis.
  • I for one LOVE splattered pancakes. They cook up so much crisper on the lower edge. In fact, I've been flipping early for years just to get this effect.
  • by mark-t (151149) <markt@ l y n x.bc.ca> on Thursday March 06, 2003 @11:21AM (#5449311) Journal
    The angular velocity is, according to the formula:

    (sqrt(pi)*1g)/(d*4)

    Where g is the accelleration due to gravity and d is the distance from the elbow to the pancake.

    In addition to the rather obvious (or at least intuitive) flaw of not considering the size/mass of the pancake, this formula cannot possibly produce the value claimed. Dimensional analysis shows that it results in an answer measured in terms of radians per second squared, and angular velocity is always measured in just radians per second.

    Of course, if they *meant* to say angular accelleration, they should have said so.

    • The problem seems to be in the interpretation of the english representation of the equation:

      The angular velocity of the object equals the square root of Pi, times the gravity divided by the distance the pancake is from the elbow times four

      You took this to be :

      (sqrt(pi)*1g)/(d*4)

      when it should be interpreted as:

      sqrt( pi*g / (d*4) )

      then you get the right units.

  • I have just had a bit of fun trying to derive the given equation. I came up with a result that is very very close.

    1) Hang-time of the pancake:
    • t=-2V/g

    2)Time for a 180 degree flip:
    • t=pi* pancakeRadius / (farEdgeVelocity-centerVelocity)

    3)Starting spin condition:
    • (farEdgeVelocity-centerVelocity)=angularVelocityAr m*pancakeRadius


    4) I can substitute equation 3 into 2 to get:
    • timeToFlip=pi* pancakeRadius/(angularVelocityArm*pancakeRadius)


    5) The pancake radius cancels out!
    • timeToFlip=pi/angularVelocityArm


    6)Then, I set the two times equal to eachother, because we are looking for the time to flip to be exactly the hang-time:
    • pi/angularVelocityArm=-2V/g


    7) Solve for angular velocity...
    • angularVelocityArm=pi*g/(-2V)


    8) The condition at Launch is :
    • angularVelocityArm=V / armRadius


    9) So, by 7 and 8, (substituting V)..
    • angularVelocityArm=pi*g/(-2* armRadius* angularVelocityArm)


    10) which is the same as ..
    • angularVelocityArm = sqrt ( pi*g/ (-2* armRadius) )


    This result is just a clean factor of two off from the article. I'm very suprised that I can put together enough physics to derive something that is apparently so newsworthy!

    now someone help me find the mistake!

It's a naive, domestic operating system without any breeding, but I think you'll be amused by its presumption.

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