1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: The dimensions of something please
Loading...