How Do You Calculate the Total Inertia Matrix for a Composite Object?

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To calculate the total inertia matrix for a composite object made of multiple parts, first, transform each part's inertia matrix to a common global coordinate system. The inertia matrices can be summed since inertia is additive. Mass terms of each part are simply added together. For parts that are not rotating about the same axis, use the parallel axis theorem to adjust their moments of inertia. This approach ensures an accurate representation of the total inertia matrix for the composite object.
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Homework Statement


The object is made out of multiple parts. The inertia matrices of every part are given. Only one part is rotating. How do I find the total inertia matrix.

Homework Equations

The Attempt at a Solution


I thought that I could sum the inertia matrices, after tranforming them to global coordinates.[/B]
 
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Inertia is additive. Mass terms are simply added. Moments of inertia are combined using the parallel axis theorem.
 

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