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Keeping a pencil standing on your hand What physics topics should I research?

  1. Jan 25, 2010 #1
    "Keeping a pencil standing on your hand" What physics topics should I research?

    Hi.

    My English is not perfect but I'll try my best. This is not a homework. It's a programming question for my simulator project.

    Scenario:
    - A pencil standing in your hand. It will fall or stand depending on how you move your hand.
    - Let's assume that the hand is just an ideal 'plane'.
    - Let's assume that a pencil is just a simple, ideal rectangular rigid body object.
    - *** Let's assume that a pencil will NOT fall on y-axis. Or in English: It will only fall to the left or right.


    Variables I have:
    - Real-time 'Acceleration' of my hand in x axis. (in m/s/s)
    - 'Mass' and 'Volume' of a pencil.

    Variables I need:
    - The change of 'theta'(angle) between the pencil and my hand(in x-axis) in each time slice. Or you could say d(theta) by d(t)

    Questions:
    What topic should I research for to relate the acceleration to the angle changes?


    note:
    *** Actually I want to do x,y and z axis but I think if I know how to solve one, I should be able to solve other too.

    Thank you in advance! Please let me know if I didn't provide enough information to the problem.
     
    Last edited: Jan 25, 2010
  2. jcsd
  3. Jan 25, 2010 #2
    Re: "Keeping a pencil standing on your hand" What physics topics should I research?

    If the pencil were perfectly balanced on its point on an ideal stationary plane (no vibration) and there was absolutely no air motion, the pencil would still fall over in a few seconds, due to the Heisenberg Uncertainty Principle. The combination of Δp (momentum) and Δx (position) in

    Δp Δx ≥ h-bar/2 means that if the initial (angular) position is fixed, the uncertainty in (angular) momentum will cause the pencil to fall over.

    Bob S
     
  4. Jan 26, 2010 #3
    Re: "Keeping a pencil standing on your hand" What physics topics should I research?

    Bob S is technically correct. However, if you consider a SMALL amount of friction between the pencil and the pivot, then Heisenberg's Uncertainty Principal can be neglected.

    First, you must tell us the mass-space distribution of the pencil.
     
  5. Jan 26, 2010 #4
    Re: "Keeping a pencil standing on your hand" What physics topics should I research?

    Either basic newtonian rigid body mechanics, or chaos theory. Not sure which one you're getting at here.
     
  6. Jan 26, 2010 #5
    Re: "Keeping a pencil standing on your hand" What physics topics should I research?

    you need to explain the situation more in depth
     
  7. Jan 26, 2010 #6
    Re: "Keeping a pencil standing on your hand" What physics topics should I research?

    lgm..
    the above replies seem focused on the initial instability...but

    you do have enough information to develop a formula for the movement of a pencil once it begins.

    Likely any introductory college course in statics and (you want this) DYNAMICS would discuss such a falling lever scenario. You'll want to relate the acceleration of the center of mass of the pencil downward from a formula like F = Ma to the movement about the base of the pencil.....the vertical (y) movement is obtained from an equation such as d=1/2at2 and I think, but am not sure, that the falling motion of the center of mass is independent of the one pencil end being "anchored"....it's been too many years since I did those kind of problems....

    anyway, the above should get you started. good luck.
     
  8. Jan 26, 2010 #7
    Re: "Keeping a pencil standing on your hand" What physics topics should I research?

    That problem was given in Sakurai, but I got 6 minutes for "reasonable" measures of icepick.
    Did you estimate that or did you actually did the math?
     
  9. Jan 26, 2010 #8
    Re: "Keeping a pencil standing on your hand" What physics topics should I research?

    You could take a look at this page for a more ideal setup than the one you describe. I'm sure it would be helpful to you.

    http://www.mathpages.com/home/kmath259/kmath259.htm
     
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