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These attached photos describe flaps which are a portion of a circle and equations are attached as the mass moment of inertia, but there are no descriptions. I am using this for part of my research, but I do not know if this was something calculated through an integral or not, but I am very unaware of this being anything related to what the mass moment of inertia would be. The equations I am given are:

$$ l=2R \frac{\sin{\alpha}}{\alpha} \\ \alpha=\pi/8 \\ I_3 = m_3 k_{y'}^2 \\ k_{y'}^2 = \frac{1}{72 \alpha} [18 \alpha^2 + 9\alpha \sin{2\alpha} - 32 (1-\cos^2{\alpha})] $$

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  • $\begingroup$ what is exactly the question? Are you interested in the derivation or an explanation? $\endgroup$
    – NMech
    Feb 26 at 17:41
  • $\begingroup$ @NMech Ah okay, sorry for the photo confusion, these are the same objects. One is a top view and one is a side view. The flap rotates along the y axis. I am not sure where they are getting this equation for the moment of inertia. I know that the moment of inertia for even part of a circle is much simpler and I tried plugging things in, but it doesn't make sense to me especially since there is no R present in the last equation. This equation may also be completely wrong, but I have no reference to prove or disprove that as I am not sure what they were able to do. $\endgroup$
    – alcopo63q
    Feb 26 at 17:47

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