The parallel axis theorem says that if the moment of inertia of a body rotating about the body's centre of mass is $I_{cm}$, then the moment of inertia of the body rotating about an axis parallel to the original axis and displaced from it a distance $d$ is $I_{S}=I_{cm}+Md^2$, where $M$ is the body's mass.

I know for a fact that this applies in cases of uniform density. Does this same theorem apply if the body's density is not uniform?

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    $\begingroup$ Yes, it does. Have a look at the proof, it doesn't assume anything about the mass distribution. $\endgroup$
    – knzhou
    Jan 12, 2016 at 17:48
  • $\begingroup$ Have you looked at how the parallel axis theorem is derived? From this the answer should be obvious. $\endgroup$ Jan 12, 2016 at 17:50
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    $\begingroup$ I'm voting to close this question as off-topic because it shows insufficient prior research $\endgroup$ Jan 12, 2016 at 17:50