Calculating the moment of inertia for a composite cylinder of different densities

Question

I am working on a project where I am using a composite cylinder composed of a cylindrical core surrounded by a cylindrical tube, where the two components have different densities. To find the total moment of inertia for the cylinder, is it enough to simply add the moments of inertia for its two components?

This sentence found on the page for "moment of inertia" on Wikipedia states that "The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis)". This leads me to believe that I can do that.

For my situation, would it simply be viable to add the moments of inertia for the cylindrical core and cylindrical tube, using their prescribed formulas? If so, why is this possible?

Sam · Answer

You can add the moment of inertia of the two objects as long the individual moments are taken along a common axis of rotation. The reason for this is that moment of inertia is a tensor. However as the rotation is about one axis only, it can be treated as a scalar. Hence you may simply take the scalar sum to find the resultant moment of inertia.

Answered by Sam on July 15, 2021

Calculating the moment of inertia for a composite cylinder of different densities

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