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Applying math to real world problems

  1. Jan 5, 2013 #1
    Equations are all well and good when you have things like "Let x = something" "Let b = the spin" "Let y = the weight" ect...

    But if you wanted to really do your own experiement at home. I have a penny on my desk, I'm sure you have all done it before but if I hold it on it's edge and then spin it, I want to measure with precision the rate at which the angle of the penny changes.

    I also want to measure the rate at which the spin slows down per second. How would someone, without any kind of computer or anything prove anything like this?

    The point I'm getting at is newton used calculus to show the orbits of planets... no technology existed then that could possibly help him.
    Last edited: Jan 5, 2013
  2. jcsd
  3. Jan 5, 2013 #2


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    Re: Appling math to real world problems...

    Do you mean theoretically? If so then (to some extent) this is a common mechanics textbook problem (IIRC, Kleppner works it out in the text itself and Morin has a problem on it). It is called Euler's disk and has been studied quite a bit actually.
  4. Jan 5, 2013 #3
    Re: Appling math to real world problems...

    Really? How accurate would you be without a calculator? I'm curious too. Math is easy without a calculator. Physics? Not a chance.
  5. Jan 5, 2013 #4


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    Re: Appling math to real world problems...

    You'll have to forgive me but I'm not understanding the question - I'm not seeing why we need a calculator.
  6. Jan 5, 2013 #5
    I got through pretty much all of my university maths courses without a calculator. The only times I found the need for one was computing with numerical methods and the occasional trig function. Most everything was pen and paper. Until you input your actual measurements, the numbers don't really matter, and when you have those, it's a simple exercise to sub them in and calculate.
  7. Jan 5, 2013 #6


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    That's weird. I calculated the orbital period of two pennies when I was about 12. I don't think calculators were common back in 1971. How on earth did I do that?

    I should re-post my paper in the physics section and get some feedback.

    Though I do recall that when I was about 14, I converted a 4 function calculator into a stopwatch. I wish I knew half as much now as when I was young.

    I once told someone that I was the ultimate nerd whilst growing up. They questioned my assertion. I should go find that guy. Like many a senile person, my childhood is slowly coming back to me....
  8. Jan 6, 2013 #7;jsessionid=a9a2P9GyK2ig

    People figure out extremely clever ways to measure things with low tech devices aided by some math.
  9. Jan 6, 2013 #8
    So show me how you would go about working this out... for those of you that can be bothered you actually have to get a real penny, spin it, write down your calculations ect. Sure you can use a calculator if you really wanted to.

    But I'm interested to see calculations for your actual spinning penny.
  10. Jan 6, 2013 #9
    Re: Appling math to real world problems...

    Isaac Newton seemed to do OK without one.
  11. Jan 6, 2013 #10
    Re: Appling math to real world problems...

    This is what I mean though... how is it possible to INVENT equations that can predict the orbit of planets?! It just seems impossible without actually being able to take a tape measure to it...
  12. Jan 6, 2013 #11


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    Re: Appling math to real world problems...

    Knowledge of geometry and mechanics, and use of observational astronomy. One only needs to be able to determine time, distance, speed/velocity, acceleration, mass. Equations are then written to describe the mechanics, and then compared to experimental (observational) measurements.

    It was also possible to measure the speed of light using geometry (surveying with reliable/accurate instruments to determine distance) and a reliable chronometer. Over time, improved methods have been developed.
  13. Jan 6, 2013 #12
    @upperkurk: You don't really need a calculator to invent equations. All you need is calculus and the ability to substitute equations to derive the kinematics equations (so inventing equations is pretty much the same as math).

    In high school, physics teachers were plugging numbers into equations that physics seemed impossible without a calculator. If I were to do a simple kinematics problem in the real world, could I get an accurate value without a calculator?
  14. Jan 6, 2013 #13


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    Re: Appling math to real world problems...

    We shouldn't also lose sight of the fact that Newton was one of the greatest geniuses to ever have lived. Despite the lack of tools that we take for granted, he came up with earth-shattering discoveries.

    What is the work of genius today is the work of tinsmiths tomorrow.
  15. Jan 6, 2013 #14
    Re: Appling math to real world problems...

    That was in his letter to Robert Hooke in February 1676. By giants, he is referring to Galileo and Kepler.
  16. Jan 6, 2013 #15


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  17. Jan 6, 2013 #16
    @OmCheeto, you say you calculated stuff like this when you were 12? Using the equation and notation I just saw in that PDF file? That stuff looks crazy difficult...

    @WannabeNewton, so if I could actually understand these equations I could grab a penny from my draw, spin it and accurately work out the angle at which the penny changes over time? Then if you were to spin it the exact same speed and have a computer measure it, I would get the same result?
  18. Jan 6, 2013 #17


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    As with any experiment you will have a margin of error but other than that you should be able to predict it up to a very reasonable approximation.
  19. Jan 6, 2013 #18


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    Going over my notes, it appears that I am incorrect. It appears that I placed the pennies a certain distance apart and calculated the time it would take gravity to bring them together in how long a time. The notes are not very good. I didn't include the original separation distance, nor the mass of the pennies.

    Gads I was a nerd.

    But I used to be able to do those calculations in my head, hence never wrote down the intermediate steps, and therefore have no clue now as how I calculated these numbers.

    I have only the equations. And given that I was using a manual typewriter probably built in the 40's, I used all manner of substitutions for the greek symbols. I substituted a lower case "w" for omega, "@" for angular acceleration, etc, etc.

    I do not recall ever taking a physics course in grades 1 through 12, so I assume I retrieved all the equations from our encyclopedia.

    Here's a clue that perhaps I had intended to solve the orbital problem:

    (please don't take note from the following. It appears I was putting together the jigsaw puzzle of physics, and made a few errors.)
    And that was it.

    These notes were transcribed in the summer of 1977, along with 11 more pages of things I thought were important. I was about to enter the Navy, and was afraid my mother would throw everything out.

    The problem of the orbit of the pennies did not re-enter my mind until yesterday. Thank you.

    *I would not discover white-out until years later.
  20. Jan 6, 2013 #19
    You must literally be a genius... At 12 years old I was playing video games and failing my times tables lol....
  21. Jan 6, 2013 #20


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    The only purchasable video game available when I was growing up was called "Pong".

    Or more specifically Odyssey, by Magnavox.

    My oldest brother bought one. Mastered it in 12 seconds.

    Boop! ....... Boop! ....... Boop!

    And as for times tables, did you not see my comment on how I was an uber-nerd?

    I sat down, during the summer, after I was told that there was more than one number base, and wrote out the multiplication tables, for all bases between 2 and 16.

    This was long before computers were available, and a bit of a while before I would realize that knowing binary and recognizing hexadecimal would become important tools in dealing with these demon machines, with which I. hmmm... Computers are awesome.

    When I got my last job, I discovered that the oldsters were using computers as if they were typewriters with TV screens. ie., They had not a clue of the inherent power of microprocessors and well written software.

    I went on to write several pieces of software for that job. I'm pretty sure it eliminated at least 3 positions over the years.

    As I've said before; "I somehow feel responsible for a bit of the unemployment problem."

    Or something like that.

    ps. I was a genius. Mostly due to long hours of mind pleasing mental massage. It was the only thing to do as a child during our long cold rainy PNW months. Now I just sit and surf in a Lay-Z-Boy recliner, and burp once in awhile. So no, I am not a patent clerk. :frown:
  22. Jan 6, 2013 #21
    uperkurk: you're being trolled so hard :P Notice the best humor 2012 PF award.
  23. Jan 6, 2013 #22


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    and the confusion sets in....

    "trolled so hard"? google google google


  24. Jan 6, 2013 #23
    Opps. Made an oopsie. I thought you were joking when you wrote "Though I do recall that when I was about 14, I converted a 4 function calculator into a stopwatch. I wish I knew half as much now as when I was young." Trolling is the art of deceiving someone.
  25. Jan 6, 2013 #24


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    Deception is the art of deceiving someone! Trolling is something else entirely!
    From wiki:

    In Internet slang, a troll (pron.: /ˈtroʊl/, /ˈtrɒl/) is someone who posts inflammatory,[1] extraneous, or off-topic messages in an online community, such as a forum, chat room, or blog, with the primary intent of provoking readers into an emotional response[2] or of otherwise disrupting normal on-topic discussion

    Trolls can use deception however. It is one of several tools.
  26. Jan 6, 2013 #25
    It seems you know quite a bit about trolling. Perhaps too much...'

    Not drawing any conclusions or anything...
    you undercover troll!
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