This topic inspired me to experiment with calculating tensors of more complex shapes of rigid bodies (I did not find them in the Mathematica database).
For simple shapes of rigid bodies, everything works great:
MomentOfInertia[Ball[{0, 0, 0}, R]];
MomentOfInertia[Cone[{{0, 0, 0}, {0, a, 0}}, R]];
MomentOfInertia[Cylinder[{{0, -1/2, 0}, {0, 1/2, 0}}, R]];
Remark: https://mathematica.stackexchange.com/a/62895/67019 The code from here also works and gives similar results.
My question: And how to calculate the inertia tensor for more complex rigid bodies. For example, for a sector of a torus or a ring with a rectangular cross section?
This picture from SolidWorks.