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Still learning dimensional analysis

  1. Jul 24, 2012 #1
    1. The problem statement, all variables and given/known data

    angular frequency omega, speed of light and gravitational constant


    2. Relevant equations

    Just the expression,

    [tex]\frac{2 \omega c}{\sqrt{G}}[/tex]

    3. The attempt at a solution

    Still learning dimensional analysis. So I am simply wanting to know if I have done this right. If I have, I get

    [tex]\frac{2 \omega c}{\sqrt{G}}[/tex]

    this with dimensions of force, right?

    Thanks in advance.
     
  2. jcsd
  3. Jul 24, 2012 #2

    cepheid

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    Re: dimensions

    I'll use square brackets around a quantity to mean, "dimensions of" that quantity (which is a fairly common notation, I think). Then:

    [ω] = time-1

    [c] = length * time-1

    [√G] = [G]1/2 = (force * length2 * mass-2)1/2

    Therefore [ωcG-1/2] = length * time-2 * force-1/2 * length-1 * mass

    = force-1/2 * mass * time-2

    = (mass * length * time-2)-1/2 * mass * time-2

    = mass1/2 * length-1/2 * time-1

    So, no, it doesn't have dimensions of force.
     
  4. Jul 26, 2012 #3
    Re: dimensions

    What does it have dimensions of then? I mean, other than what you have said, is there a commonly known dimension it exhibits? like energy for instance?
     
  5. Jul 26, 2012 #4

    cepheid

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    Re: dimensions

    It doesn't correspond to any common physical quantity, and there is no reason that it has to (you've simply come across a new type of quantity),

    However, the *square* of the quantity is a common type of quantity. Hint: square everything in blue, and rearrange things to produce "force" plus some leftover stuff. What is the dimension of the quantity you've come up with?
     
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