Lagrangian about rolling disk on a horizontal plane

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SUMMARY

The discussion centers on the application of Lagrangian mechanics to a rolling disk on a horizontal plane, specifically referencing exercise 1.11 from Goldstein's "Classical Mechanics." Participants question the omission of rotational kinetic energy in the solution, emphasizing that the Lagrangian should include both translational and rotational components, represented as L = T = 1/2 mx^2 + 1/2 I w^2. The importance of incorporating the term 1/2 I w^2 is highlighted for a complete understanding of the system's dynamics.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with rotational dynamics
  • Knowledge of kinetic energy equations
  • Basic principles of classical mechanics as outlined in Goldstein's textbook
NEXT STEPS
  • Review the derivation of the Lagrangian for rolling objects
  • Study the concept of rotational kinetic energy in detail
  • Explore examples of Lagrangian mechanics applied to different systems
  • Investigate the implications of neglecting rotational components in dynamic systems
USEFUL FOR

Students of classical mechanics, physics educators, and anyone studying Lagrangian dynamics, particularly in the context of rolling motion and energy conservation principles.

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Homework Statement



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Homework Equations

The Attempt at a Solution



This is the problem in Goldstein's classical mechanics exercise 1.11
I wonder why the solution doesn't consider rotational kinetic energy (1/2 I w^2)
So, L= T = 1/2mx^2 + 1/2 I w^2 .
 
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