Classical Mechanics & Special Theory of Relativity

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Lectures

      Classical Mechanics

      • Lecture 1. [Intertial Systems]
      • Lecture 2. [Uniformly Accelerated System]
      • Lecture 3. [EOM in Rotating Frames]
      • Lecture 4. [Motion on Earth Surface]

      Special Theory of Relativity

      • Lecture 0. [Invitation to Special Relativity]
      • Lecture 1. [Infamous Experiments]
      • Lecture 2. [Einstein's Postulates]
      • Lecture 3. [Lorentz Transformation]
      • Lecture 4. [Mass-Energy Equivalence]
      • Lecture 5. [Relativistic Dynamics]
      • Lecture 6. [Relativistic Energy-Momentum]
      • Lecture 7. [Collisions]
      • Lecture 8. [Tensors]
      • Lecture 9. [Four Vector Notation]
      • Lecture 10. [P.H.L.G.]
      • Lecture 11. [Minkowski Force]

Numerical Problems

Remarks

  1. Watch : Dissociation of Comet Shoemaker–Levy 9.
  2. Watch : Macroscopic reversibility in Non-Newtonian fluid.
  3. Be careful about tensor indices. Practice problems from Spiegel/Arfken-Weber Book (and NOT from Kleppner-Kolenkow).
  4. When solving assignments, whenever applicable, draw neat & physical diagram of events and explain the symbols. Read the question carefully and after solving the problem, frame and write to-the-point answer asked in the question.
  5. Video-lecture on Orthogonal Transformation (OT).
  6. Video-lecture on Proper Homogeneous Lorentz Group (PHLG).
  7. Tensor Properties and application.

Topics

  1. Classical Mechanics:
    • Non-inertial frame: Non-inertial frames and idea of fictitious forces. E.O.M with respect to a uniformly accelerating frame. E.O.M with respect to a uniformly rotating frame - Centrifugal and Coriolis forces. Applications: Surface of a rotating liquid, deflection of falling mass, cyclone.
  2. Special Theory of Relativity:
    • Michelson-Morley Experiment and its outcome: Postulates of Special Theory of Relativity. Invariance of Special Theory of Relativity. Invariance of space-time interval. Derivation of Lorentz transformation equations. Length contraction. Time dilation. Simultaneity and order of events. Concept of causality. Relativistic transformation of velocity. Velocity Addition. Relativistic Dynamics. Energy-momentum dispersion relation. Massless particles. Mass-energy Equivalence. Transformation of Energy and Momentum.
    • Introduction to Tensor Analysis: Definition of cartesian tensors in 3 dimensions. Transformation properties. Contraction of tensors in 3 dimensions.
    • Relativity in Four Vector Notation: Minkowski space time [(ct,x,y,z)] or [(x,y,z,ct)] diagram.

Study Materials

  1. Non-Inertial Frames:
    • An Introduction to Mechanics - D. Kleppner, R.J. Kolenkow.
    • Mechanics - Berkeley Physics (Vol.1) - C.Kittel, W.Knight et.al.
    • Theoretical Mechanics - M.R. Spiegel.
    • Fundamentals of Physics - Resnick, Halliday and Walker.
  2. Einsteinian Relativity:
    • Introduction to Special Relativity - R. Resnick (Main Book).
    • Special Relativity (MIT Introductory Physics) - A.P. French.
    • The Special Theory of Relativity - Banerji and Banerjee.
    • Modern Physics - A.Beiser/Mani-Mehta.
    • Special Theory of Relativity - J.H.Smith/D.Bohm/N.D.Mermin/D.Morin/A.Einstein.
  3. Poincarian Relativity:
    • Classical Electrodynamics - J.D. Jackson.
    • Classical Theory of Fields (Vol II) - Landau and Lifshitz.
    • Tensor Analysis - Barry Spain.
    • Mathematical Physics - Arfken-Weber/Murray Spiegel/S.D.Joglekar.