Moments of inertia for solids of revolution and variational methods

Details Moments of inertia for solids of revolution and variational methods Moments of inertia for solids of revolution and variational methods

2005-07-23

arxiv.org/abs/physics/0507172v2

Eur. J. Phys. 27 (2006) 183-192

Physics

Physics Education

6 pages, 6 figures, LaTeX2e. Two paragraphs added. Minor typos corrected. Version to appear in European Journal of Physics

Scientific paper

10.1088/0143-0807/27/2/001

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 a 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.

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