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Dynamics of Rotational Movements

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Lecture Notes on Newtonian Mechanics

Part of the book series: Undergraduate Lecture Notes in Physics ((ULNP))

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Abstract

In this chapter we discuss the dynamics of rotational movements. The main object of study is the rotational dynamics of a solid body, but we will also consider the rotational movement of a particle or a system of particles. As we shall see in what follows, the dynamics of rotational motion has many analogies with the dynamics of the translational motion. At the same time, there are important differences, in part because of the cyclic nature of the angular variable. This property means that after increasing the value of the variable for a certain period (equal to \(2\pi\) in case of an angle), the body comes back to the same position. We will formulate the laws of rotational dynamics and find the corresponding conservation law.

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Notes

  1. 1.

    The theorem works also for three-dimensional bodies with the property that each of its plane sections orthogonal to \(\alpha _{0}\) has the center of mass belonging to \(\alpha _{0}\) . A more general formulation is possible in Analytical Mechanics [11, 21].

  2. 2.

    The correct analysis of the magnetic forces can only be done in the scope of Relativistic Electrodynamics [17, 23]. This consideration shows a perfect agreement with the law of conservation of angular momentum.

References

  1. R. Abraham, J.E. Marsden, Foundations of Mechanics (AMS Chelsea, Providence, 2008)

    Google Scholar 

  2. G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists (Academic, San Diego, 1995)

    Google Scholar 

  3. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1989)

    Google Scholar 

  4. V.I. Arnold, Ordinary Differential Equations, 3rd edn. (Springer, 1997)

    Google Scholar 

  5. J. Barcelos Neto, Mecânica Newtoniana, Lagrangiana & Hamiltoniana (Editora Livraria da Física, S\(\tilde{\mathrm{a}}\)o Paulo, 2004)

    Google Scholar 

  6. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge Mathematical Library, Cambridge University Press,Cambridge/New York, 2000)

    Google Scholar 

  7. M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics. Texts in Applied Mathematics, vol. 11, 4th edn. (Springer, New York, 1992)

    Google Scholar 

  8. H.C. Corben, P. Stehle, Classical Mechanics (Dover, New York, 1994)

    Google Scholar 

  9. E.A. Desloge, Classical Mechanics, vols. 1 and 2 (Wiley, New York, 1982)

    Google Scholar 

  10. F.R. Gantmacher, Lectures in Analytical Mechanics (Mir Publications, Moscow, 1975)

    Google Scholar 

  11. H. Goldstein, C.P. Poole, J.L. Safko, Classical Mechanics, 3rd edn. (Addison Wesley, San Francisco, 2001)

    Google Scholar 

  12. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, 7th edn. (Elsevier, Burlington, 2007)

    Google Scholar 

  13. R.A. Granger, Fluid Mechanics. Dover Books on Physics (Dover, New York, 1995)

    Google Scholar 

  14. D. Gregory, Classical Mechanics (Cambridge University Press, Cambridge, 2006)

    Google Scholar 

  15. W. Greiner, Classical Mechanics: Point Particles and Relativity. Classical Theoretical Physics (Springer, New York/London, 2003)

    Google Scholar 

  16. I.E. Irodov, Mechanics. Basic Laws. (in Russian) (Nauka, 6 Ed., 2002); I.E. Irodov, Problems in General Physics (Mir Publications, 1988 and GK Publisher, 2008)

    Google Scholar 

  17. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1998)

    Google Scholar 

  18. J.V. José, E.J. Saletan, Classical Dynamics: A Contemporary Approach (Cambridge University Press, Cambridge/New York, 1998)

    Google Scholar 

  19. T.W.B. Kibble, F.H. Berkshire, Classical Mechanics (World Scientific, River Edge, 2004)

    Google Scholar 

  20. C. Lanczos, The Variational Principles of Mechanics (Dover, New York, 1970)

    Google Scholar 

  21. L.D. Landau, E.M. Lifshits, Course of Theoretical Physics: Mechanics, 3rd edn. (Butterworth-Heinemann, 1982)

    Google Scholar 

  22. L.D. Landau, E.M. Lifshitz, Hydrodynamics. Course of Theoretical Physics Series, vol. 6, 2nd edn. (Butterworth-Heinemann, 1987)

    Google Scholar 

  23. L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields. Course of Theoretical Physics Series, vol. 2

    Google Scholar 

  24. N.A. Lemos, Mecânica Analítica, 2nd edn. (Livaria da Física, 2007)

    Google Scholar 

  25. Y.-K. Lim, Problems and Solutions on Mechanics: Major American Universities Ph.D. Qualifying Questions and Solutions (World Scientific, Singapore/River Edge, 1994)

    Google Scholar 

  26. J.B. Marion, S.T. Thornton, Classical Dynamics of Particle and Systems (Harcourt, Fort Worth, 1995)

    Google Scholar 

  27. D. Morin, Introduction to Classical Mechanics with Problems and Solutions (Cambridge University Press, Cambridge/New York, 2008)

    Google Scholar 

  28. P.M. Morse, H. Fishbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953)

    Google Scholar 

  29. I.L. Shapiro, Lecture Notes on Vector and Tensor Algebra and Analysis (CBPF, Rio de Janeiro, 2003)

    Google Scholar 

  30. A. Sommerfeld, Mechanics. Lectures on Theoretical Physics, vol. 1 (Academic, New York, 1970)

    Google Scholar 

  31. K. Symon, Mechanics, 3rd edn. (Addison Wesley, Reading, 1971)

    Google Scholar 

  32. J.R. Taylor, Classical Mechanics (University Science Books, Sausalito, 2005)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Fisica – ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil

    Ilya L. Shapiro & Guilherme de Berredo-Peixoto

  2. Tomsk State Pedagogical University, Tomsk, Russia

    Ilya L. Shapiro

Authors
  1. Ilya L. Shapiro
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  2. Guilherme de Berredo-Peixoto
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Shapiro, I.L., de Berredo-Peixoto, G. (2013). Dynamics of Rotational Movements. In: Lecture Notes on Newtonian Mechanics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7825-6_8

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