# Calculate Inertial tensor of 5000 points

1. Jan 21, 2013

### Yuriick

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

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

3. The attempt at a solution

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

R = $\frac{1}{5000}$$\sum r_{i}$

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. Jan 21, 2013

### bjnartowt

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?