Mass moment inertia of object displaced from axiz

AI Thread Summary
The discussion focuses on calculating the mass moment of inertia for an object displaced from its axis of rotation. The user considers two methods: developing an integral for mass distribution or using the parallel axis theorem. The consensus leans towards using the integral approach, as it simplifies the computation given the object's orientation. The parallel axis theorem is acknowledged but deemed more complex for this scenario. Overall, the integral method is recommended for its straightforwardness in this context.
PTC
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Hey y'all,

A plea for general advice here as I embark on a project. Say I have an object rotating around an axis but *displaced* some distance "r" from that axis. It's length, a dimension perpendicular to the axis, is "a." I'm interested in finding the mass moment of inertia for the object. As I see it, I have two choices: (1) develop an integral describing the mass distribution of the object around the axis and then use the fundamental theorem and the interval r to r+a or; (2) use the parallel axis theorem, that is, develop definitive integrals describing both the mass distribution of the object at r=0 and around the axis at r->r+a, summing the two. So real simply, fundamental theorem or parallel axis theorem?

Thanks!

PTC
 
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I never really got my head round the parallel axis theorem, so I would use 1), which should be fairly easy, since the object is pointing straight away from the axis, it makes the integral fairly simple.
 
Thanks, Bruce! That's just about what I figured--it'd be much easier to compute over the interval. Thanks again!

PTC
 

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