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If the cylinder's cross-section is as followed: enter image description here

Assuming that the bottom part of the cylinder is filled because it is filled with water. What would be the moment of inertia about the center of the circle? (Assume that the cylindrical case that contains the water has no mass).

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    $\begingroup$ The moment of inertia is only defined for a rigid body, one whose constituent masses can't move relative to each other. If you really mean that it's filled with liquid water, then this isn't a rigid body. $\endgroup$
    – Michael Seifert
    Jan 22 at 14:20
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    $\begingroup$ Also, by "three quarters full" do you mean that the water level is three quarters of the way from the bottom to the top? Or do you mean that the volume of the water is three quarters of the total volume? The two are not equivalent. $\endgroup$
    – Michael Seifert
    Jan 22 at 15:39
  • $\begingroup$ @Michael Seifert The moment of inertia can be defined at a given instant also for a non-rigid body. However the formulas of rigid body mechanics obviously assume that the bodies are rigid! $\endgroup$
    – Valter Moretti
    Jan 22 at 17:09
  • $\begingroup$ @Michael Seifert I meant that the volume of the water is three quarters of the total volume $\endgroup$
    – DSONSD
    Jan 23 at 5:10

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