[Physics] how to increase the moment of inertia of a hollow aluminium pipe without changing the outer diameter

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how to increase the moment of inertia of a hollow aluminium pipe with external diameter fixed and only allowed to change the shape of internal section for example rectangular hole or extruded section

Best Answer

All things being equal, the contribution of a mass element to the total moment of inertia about a given axis increases as the square of its distance from the axis of rotation. Basically, you want to put as much mass as possible as far away from the rotational axis as possible.

Since your question appears to imply that the axis of rotation is the center axis of the pipe, the answer is simple: an ordinary thick-walled cylindrical shell (aka common pipe) maximizes the moment of inertia. You can find the corresponding formula here. Since the the outer diameter is given, you only need to find the inner radius, which depends on how much aluminium per length of pipe you're allowed.