I know this is true for things with even dispersed mass, when each infinitesimal has actually the same mass about the axis you space considering. Yet is it additionally true because that non-uniform mass.

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Even simply a short, correct, answer would certainly be great. I was unable to uncover this everywhere online.

By parallel axis theorem, the moment of inertia need to be minimum about an axis passing v the CM, no issue it"s symmetric or not.

For intend the minute of inertia around a certain axis i m sorry does no pass v its centimeter is $I$, then by parallel axis theorem, the moment of inertia with respect to a parallel axis through the centimeter is $I - Mh^2$ where $M$ is the total mass of the object and $h$ is the distance between the 2 axes.

As for minute of inertia around points, due to the fact that they space tensors, it relies on exactly how you define large and small.

The parallel axis theorem states that minute of inertia around an axis parallel come the minute of inertia about an axis passing through COM is given by $$I=I_cm+Mx^2$$ so obviously MOI is minimum about an axis passing v COM

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