For example, on Wikipedia, I am given the formula $$I = (m/6)(P.P+P.Q+Q.Q) $$ to calculate the moment of inertia for a triangle with points origin, $P$, and $Q$. If I were to have two triangles bound together on origin and $P$ or $Q$, could I add the two moment of inertia together?
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1$\begingroup$ Yes. $\hspace{0mm}$ $\endgroup$– knzhouCommented Aug 9, 2016 at 5:33
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$\begingroup$ @knzhou What if they were bound at any point(s), for example P and Q (not origin) $\endgroup$– JavaProphetCommented Aug 9, 2016 at 5:34
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$\begingroup$ Sure. As long as you're always taking the moment of inertia about the same point (the origin) it's still cumulative. $\endgroup$– knzhouCommented Aug 9, 2016 at 5:40
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Shortly: Yes
The reason is that to calculate the moment of inertia we take the sum of all point masses multiplied by the square of their respective distance from the axis of rotation. $$ I=\sum_{i=0}^N m_i r_i^2 $$ So the physics are the same if you have one, two or many such triangles (as long as you are rotating everything around the same axis.
on a side note, to add moments of inertia of objects given for center of mass rotation when the rotation is not around the center of mass of the individual objects, use the Parallel Axis Theorem
