The Virial Theorem and its applications in the （维里定理及其应用）.pdf

The Virial Theorem and its applications in the teaching of Modern Physics Celso L. Ladera, Eduardo Alomá y Pilar León Departamento de Física, Universidad Simón Bolívar, Apdo. 89000, Caracas 1086, Venezuela . E-mail: clladera@usb.ve (Received 18 February 2010; accepted 18 May 2010) Abstract The Virial Theorem is receiving scarce attention in the teaching of classical mechanics, and intermediate mechanics and in general physics courses. In this work we present a proposal for including this theorem in the contents of Gravitation or Kinetic Theory of Gases in general physics courses, and we illustrate the importance of the theorem with a sample set of applications in mechanics, introductory quantum mechanics, thermodynamics and astrophysics. Two relevant cases, the applications of the theorem to the presence of the so-called dark matter in the Universe, and to the study of the stability condition of the driven inverted pendulum are presented. Keywords: Virial Theorem, Teaching of Classical Mechanics, Dark Matter, Inverted Pendulum. Resumen El Teorema del Virial está recibiendo escasa atención en la enseñanza de la física general, de la mecánica intermedia y de la mecánica clásica. Este trabajo presenta una propuesta para la enseñanza de este teorema en el estudio de la Gravitación o en la Teoría Cinética de Gases a nivel de física general universitaria, y se demuestra su importancia con aplicaciones en mecánica, mecánica cuántica, termodinámica y astrofísica. Como casos importantes se presenta la aplicación de este