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Moment of Inertia vs. Inertia Constant

  1. Jun 17, 2014 #1
    The following equations are found in the following reference (Page 119):

    http://www.eeh.ee.ethz.ch/fileadmin/user_upload/eeh/studies/courses/power_system_dynamics_and_control/Documents/DynamicsPartI_lecture_notes_2012.pdf

    By definition, the inertia constant for a synchronous machine is defined as

    [tex] H = (1/2 J \omega_0^2) / S [/tex]

    where

    [tex] a) H= \text{constant of inertia } (s) [/tex]
    [tex] b) S = \text{rated power of synchronous machine } (MW) [/tex]
    [tex] c) \omega_0 = \text{nominal angular frequency } (rad/s) [/tex]
    [tex] d) J = \text{moment of inertia for rotor } (kg m^2) [/tex]

    I.e.

    [tex] J = 2HS/\omega_0^2 [/tex]

    can be used to find the moment of inertia. Based on the units of a), b) and c) the unit of J is

    [tex] s MW/(rad^2/s^2) [/tex]

    However, i cannot see that this is the same as kg/m^2, as the result is supposed to yield from d). Can anyone help me?
     
  2. jcsd
  3. Jun 17, 2014 #2

    D H

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    Hint #1: Radians are unit less, so you can drop that term.
    Hint #2: The watt (and hence megawatts) is a derived unit. What are its primitive units?
     
  4. Jun 17, 2014 #3
    Hint #3: Instead of using MW (megawatts) you should just use W (watts). M is just a numerical factor of 1000000 and therefore is unitless. The Watt is the standard unit of power for the metric system.
     
  5. Jun 17, 2014 #4
    There is no reference to this on page 119.

    However, the quantity defined in your post have units of seconds (energy/power).
    The confusion may be due to the fact that (at least) two different quantities may be called the same name: "inertia constant".

    See for example here:
    http://books.google.ca/books?id=Su3...onepage&q=inertia constant of machine&f=false

    You are talking here about the second quantity, the H defined on page 540 of that book and not the first one (I*ω) which is also called inertia constant, on the same page.
     
  6. Jun 18, 2014 #5
    I do not understand why Radians are unit less. Can anyone explain this? Thanks for the answers.
     
  7. Jun 18, 2014 #6
    Because you divide [Length] by [Length]

    θ = s /r

    s is arc length (of a circle)
    r is radius

    EDIT:

    This page has a nice graphical (animated) explanation about the radian:
    http://ru.wikipedia.org/wiki/Радиан
     
    Last edited: Jun 18, 2014
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