Moments of inertia for solids of revolution and variational methods

We present some formulae for the moments of inertia of homogeneous solids of revolution in terms of the functions that generate the solids. The development of these expressions exploits the cylindrical symmetry of these objects and avoids the explicit use of multiple integration, providing an easy a...

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Bibliographic Details
Published in:European journal of physics 2006-03, Vol.27 (2), p.183-192
Main Authors: Diaz, Rodolfo A, Herrera, William J, Martinez, R
Format: Article
Language:English
Subjects:
Communication, education, history, and philosophy
Exact sciences and technology
General physics
Physics
Physics literature and publications
Surveys and tutorial papers, resource letters
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Summary:We present some formulae for the moments of inertia of homogeneous solids of revolution in terms of the functions that generate the solids. The development of these expressions exploits the cylindrical symmetry of these objects and avoids the explicit use of multiple integration, providing an easy and pedagogical approach. The explicit use of the functions that generate the solid gives the possibility of writing the moment of inertia as a functional, which in turn allows us to utilize the calculus of variations to obtain new insight into some properties of this fundamental quantity. In particular, minimization of moments of inertia under certain restrictions is possible by using variational methods.
ISSN:0143-0807
1361-6404
DOI:10.1088/0143-0807/27/2/001