1. Not finding help here? Sign up for a free 30min 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!

Point Mass Inertia Tensor

  1. Dec 18, 2012 #1
    1. The problem statement, all variables and given/known data

    A)Find the moment of inertia tensor for a system of 4 particles of mass 1kg at A=(1,1,0), B=(1,-1,0) C=(-1,1,0) D=(-1,-1,0) in Cartesian coordinates.

    B)Rotate the coordinates 30 degrees around the z axis and find the tensor in the new coordinates.

    2. Relevant equations

    Ixx=[itex]\sum[/itex]y^2+z^2
    Iyy=[itex]\sum[/itex]x^2+z^2
    Izz=[itex]\sum[/itex]y^2+x^2
    Ixy=[itex]\sum[/itex]xy
    Iyx=[itex]\sum[/itex]yx
    Izx=[itex]\sum[/itex]zx
    Izy=[itex]\sum[/itex]zy

    I'=RIR*

    3. The attempt at a solution
    I get Ixx=4, Iyy=4, and Izz=8. Anything multiplying z is 0 and all the xy components cancel out. So a diagonal matrix.

    For B I just apply the z rotation matrix with 30,RIR*, but when I do this I get the same thing. This can't be right so I either calculated my starting matrix wrong or am rotating incorrectly.
     
  2. jcsd
  3. Dec 18, 2012 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hi darthmonkey. Maybe the tensor components don't change under the rotation! Have you tried figuring out the new coordinates of the particles in the rotated system and then calculating the components of the tensor from these components?
     
  4. Dec 18, 2012 #3
    Haha, thanks. I got it to all work out.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Point Mass Inertia Tensor
  1. Inertia tensor (Replies: 1)

  2. Inertia tensor (Replies: 1)

  3. Inertia tensor (Replies: 2)

  4. Inertia tensor (Replies: 2)

Loading...