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Homework Help: The dimensions of something please

  1. Jun 8, 2012 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    I read about this expression for the Coriolis force

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

    Would I be right in saying this has dimensions of force?

    Thank you!
  2. jcsd
  3. Jun 8, 2012 #2
    Oh, omega is angular frequency, I believe. c is the speed of light and G is newtons constant.
  4. Jun 8, 2012 #3
    The dimensions of force are mass times length over time squared; let's call that [itex]F = ML/T^2[/itex]. Velocity is [itex]v = L/T[/itex]. What would frequency be, then, and the square root of the gravitational constant?
  5. Jun 8, 2012 #4
    So, what I have is angular frequency times the speed of light over the gravitational constant, so what you are saying is that

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

  6. Jun 8, 2012 #5
    I haven't said anything of the kind. I'm asking you what the dimensions are of [itex]\omega[/itex] and [itex]G[/itex]. The first one should be easy; the second might be a little harder, but as a hint, use Newton's force law for gravitation.
  7. Jun 8, 2012 #6
    I am still learning this dimension stuff, so don't expect me to be overly useful.

    Newtons force law is mass x m/s/s yes? So how does this help me? I don't know the dimensions to angular frequency... is it just a frequency?

    I see one link saying it is M^0L^0T^-1

    so what is this for frequency, just 1/time? So how will this help me? I don't even know how to calculate terms like these together?
  8. Jun 8, 2012 #7
    G just has dimensions of speed squared? Or that was what someone told me once. Is that true?
  9. Jun 8, 2012 #8
    Frequency is 1/time, yes.

    Newton's law of gravitation is [itex]F = Gm_1 m_2/r^2[/itex] In the language of dimensions, that's force = G x (mass) x (mass) / (length x length). Knowing the dimensions of force already, you should be able to solve for the dimensions of G.
  10. Jun 8, 2012 #9
    I'm clueless how to. I don't know how you calculate terms... I can solve for G... that is easy...

    [tex]Fr/m^2 = G[/tex]

    So.... now what?
  11. Jun 8, 2012 #10
    That's [itex]r^2[/itex].

    You need to plug in the dimensions of force now.
  12. Jun 8, 2012 #11
    Sorry, treat for r^2. Forgot that... now what do you mean I need to plug in for force? I am alien to this... helping me with a working example would be much more educational for me... This is total chinese for me.
  13. Jun 8, 2012 #12
    Let's think about this more concretely.

    You measure lengths in meters. You measure time in seconds and mass in kilograms. You measure force in newtons, where 1 newton = 1 kg m/s/s.

    Take what you just wrote:

    [itex]F r^2 /m^2 = G[/itex]

    And convert it to units. "Force -> newtons" for instance. [itex]r^2[/itex] -> meters squared, and so on.

    [itex](\text{newtons}) (\text{meters})^2 / (\text{kilograms})^2 = G[/itex]

    But you know that newtons can be expressed in terms of kilograms, meters, and seconds, right?
  14. Jun 8, 2012 #13
    right... I think I am following... now?
  15. Jun 8, 2012 #14
    How do you calculate something like

    Newtons x meters^2

    I need to be shown before I can do it.
  16. Jun 8, 2012 #15
    Newtons = kilograms x meters / (seconds)^2
  17. Jun 8, 2012 #16
    Then how would you divide it by kilograms^2... I would believe there is some kind of special conversion formula to get from newtons to the rest right?
  18. Jun 8, 2012 #17
    It's perfectly fine to leave one power of kilograms in the denominator.
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