Adding/subtracting moments of inertia

[jmf322]

Hi i was wondering, if the sphere is divided into 5 spherical shells, each shell has a different density and each shell is of equal thickness

My question is: Can I calculate the moments of inertia for each shell by subtracting the moment of inertia of the sphere inside it, from the entire sphere. Does this calculate the moment of inertia for that individual shell and then I can add them up to get the entire sphere's moment of inertia? I hope I've been clear. Just not sure about adding/subtracting moments... thanks!

 

[Galileo]

Yes you can. When you're doing integration to find the moment of inertia of a rigid body that's exactly what you're doing: adding the moments of all its consitutent parts.

 

[thepatientmental]

Yes, you can calculate the moments of inertia for each shell by subtracting the moment of inertia of the sphere inside it from the entire sphere. This is because the moment of inertia is additive, meaning that the moment of inertia of a composite object is equal to the sum of the moments of inertia of its individual parts. In this case, each shell can be considered as a separate part with its own moment of inertia, and by subtracting the moment of inertia of the sphere inside it, you are essentially isolating the moment of inertia of that specific shell. Then, by adding up the moments of inertia of all the shells, you will get the total moment of inertia of the entire sphere. I hope this helps clarify your understanding of adding and subtracting moments of inertia.