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 of curved cuboid

  1. Oct 18, 2011 #1
    Hi Physics Forums!

    Moment of inertia question for you:
    I have a cuboid, like the first one in this link

    http://en.wikipedia.org/wiki/List_of_moments_of_inertia

    only it is curved around the y (w in pic) axis such that the x (h in pic) axis touches the top and bottom ends of the cuboid and it is a parabolic curve that satisfies the following:
    z=r*(1-(x^2)/((c/2)^2))
    where r is the distance from the origin to the center of the cuboid and c is the chord length (in the x direction)
    I need to find what the moment of inertia components would be, and I'm stumped. Any help would be greatly appreciated.
     
  2. jcsd
  3. Oct 18, 2011 #2
    I can't picture what you're describing. If you can provide a sketch then I can probably figure it out.

    If the shape is a 2D "extrusion" then it is sufficient to find the inertia of the 2D slice which should be a simple region in R2.
     
  4. Oct 19, 2011 #3
    Thanks for the reply. I have made a simple 2D sketch for you. The y axis is coming out of the page. Technically it is more like a flat plate than a cuboid but I would like to find the xx yy zz components of inertia if possible.
     

    Attached Files:

  5. Oct 20, 2011 #4
    Ok this is simple. For Iyy do double integral of x^2 + z^2 dA on the region -c/2<x<c/2 and 0<z<z(x). This gives moment of inertia about the origin.
     
  6. Oct 20, 2011 #5
    Okay, and I think the Izz will stay the same as a regular cuboid, right? What about Ixx? And for z(x) I use r*(1-(x^2)/((c/2)^2)) right? And should it be dm instead of dA for mass moment of inertia?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Moment of inertia of curved cuboid
  1. Moments of inertia (Replies: 1)

  2. Moment of Inertia (Replies: 2)

  3. Moment of inertia (Replies: 70)

Loading...