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Calculate Inertial tensor of 5000 points

  1. Jan 21, 2013 #1
    1. The problem statement, all variables and given/known data

    I was given a sample of 5000 points from an ellipsoidal blob (in 3D) that has some orientation. Assuming that each point has equal mass, I was asked to calculate the inertia tensor of this blob, then find the principal axes to determine the orientation of this blob.


    2. Relevant equations

    R = [itex]\frac{1}{M} [/itex][itex]\sum m_{i}r_{i}[/itex]
    where M is the sum of the masses of every point
    R is the center of mass

    I = - [itex]\sum m_{i} [r_{i} - R][r_{i} - R][/itex]

    3. The attempt at a solution

    Since all the mass for every particle is the same, the formula for center of mass becomes,

    R = [itex]\frac{1}{5000} [/itex][itex]\sum r_{i}[/itex]

    however I'm not sure how to find the inertial tensor since I don't know the mass of each particle.

    Any help would be much appreciated, thanks!
     
  2. jcsd
  3. Jan 21, 2013 #2
    Perhaps you do not know the mass of each particle (in your line with the CM, you seem to assume that every mass is of mass "m", therefore, M = 5000*m). Why not scale out this unknown m, adn compute I/m? I bet you know all the r_i from your initial data set, and it seems like you can compute R. Is there a more complicated thing stopping you, even in light of this simple suggestion?
     
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