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While I was trying to find out the mass moment of inertia of an elliptical ring I got struck and could not think about as to what I must do. I tried integrating but the radius keeps changing from semi major to semi minor. I have also tried using the perpendicular axis theorem but again the maths is starting to go over my head. and despite all of this I haven't come any closer to anything that remotely looks like a solution to my problem.

I am also unable to guess as for what kind of piece of the ellipse shaped ring I should take so as to integrate them to find out the moment of inertia

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    $\begingroup$ Keep working at it. It won't help you for us to do it for you. And about which axis are you trying to calculate it? $\endgroup$ – Bill N Sep 23 '16 at 17:24
  • $\begingroup$ Interesting question. Please show your work. For some shapes the integral will be difficult. $\endgroup$ – sammy gerbil Sep 23 '16 at 22:49
  • $\begingroup$ Probably not that difficult actually. You can work it out from the area moment of inertia for an ellipse by differentiating wrt $a$ and $b$, or subtracting MI for ellipse with axes $(a,b)$ from one with axes $(a+\delta a, b+(b/a)\delta a)$. $\endgroup$ – sammy gerbil Sep 24 '16 at 14:33