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!

Moment of inertia in n dimensions.

  1. Dec 10, 2011 #1
    I've just been thinking about moments of inertia in n dimensions and I just want to establish if this makes any sense:

    I'm considering doing a Monte Carlo evaluation of the moment of inertia of any n-ball - a solid sphere in n dimensions. Now I think you can say that the moment of inertia of a sphere in 2d space - a circle - is (1/2)mr^2, this being about an axis through the centre, which in 2d space is merely the point in the centre. Now it is pretty run of the mill to integrate a circle like this in 3d space to get the moment of inertia of a sphere (or at least you're integrating an infinitesimally thin cynlinder). My question is - are the notions of mass and density in 3d the same as in 2d (and presumably by extension in all dimensions)? What is the exact relationship between a 2d "mass" or "density" and a 3d one? For one thing, density in 2d would have to have different units than in 3d. What exactly would a 2d mass be?

    Of course it's possible that none of this makes any sense. After all, you can't really have mass in two dimensions, can you?
     
    Last edited: Dec 10, 2011
  2. jcsd
  3. Dec 10, 2011 #2

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Possibly useful:
    http://books.google.com/books?id=8vlGhlxqZjsC Tensor Calculus by Synge and Schild
    Search for moment of inertia and get to page 161 to read about the fourth-order moment of inertia tensor in N-dimensions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Moment of inertia in n dimensions.
  1. Moment of Inertia (Replies: 3)

Loading...