Can Volume Moments Be Converted to Mass Moments for Non-Uniform Density Objects?

[Fn4]

Hello,

I was wondering if some one would be able to check my thought process on this.

I have an object ( a boat) which I'm only able to calculate the tensors of the volume moment around its volume centroid. If i assume that the object has a uniform density ( which it does not, just bear with me here), and i multiply the density by the volume moments tensors ( L^5 X M/L^3 = ML^2) it will give me the mass moments tensors. And If i use the parallel axis theorem https://en.wikipedia.org/wiki/Parallel_axis_theorem and the tensor generalization to shift the location to the CG, would this give me a a fairly accurate value for the Mass moment tensors about the CG ( even though the boat does NOT have uniform density)??

And one last thing, is the Ri and Rj in the tensor generalization formula vectors or just magnitudes?

Best
Fn4

 

[Simon Bridge]

You can test this by guessing the non-uniform density to be such that all the mass of the boat is in the stern and do the maths.
Similarly, test Ri and Rj to see what happens if you assume they are vectors and if you assume they are magnitudes.
Don't be scared to try stuff out.