Supplementary text book for additional reading: Classical Mechanics, by John R. Taylor

Old Examinations

Topics Covered:
• Vectors, addition of vectors, unit vectors, components of a vector (in Cartesian coordinates), Scalar (dot) product and vector (cross) product of two vectors.
• Basic description of motion: position vector, displacement, velocity, momentum, acceleration, description of motion with constant acceleration.
• Uniform circular motion (angular velocity and radial acceleration), polar coordinates in 2 dimensions, general 2-dimensional motion in polar coordinates, radial and angular components of velocity and acceleration.
  Relevant Sections in the Book: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.9 (important, upto page 37)

Topics Covered:
• The need for reference frames, Newton's first law of motion, the concept of inertial and non-inertial reference frames, isolated bodies.
• Newton's second law of motion, unit of force, principle of superposition, interaction as the origin of force, non-inertial frames and the concept of fictitious forces.
• Newton's third law of motion, action and reaction
• Some common examples of force: Newton's law of gravitation, gravity due to empty and solid spherical shells (no derivations), weight, acceleration due to gravity.
• Linear restoring force (Hooke's law), Motion under a linear restoring force (Simple Harmonic Motion): general solution of the simple harmonic equation, the concept of initial conditions, time period and frequency of the oscillations.
• Contact forces: tension on a string, normal force (perpendicular to a surface), friction
  Relevant Sections in the Book: 2.1, 2.2, 2.4, 2.5 (topics on pulleys and viscocity not included)
  Relevant Examples: 2.3, 2.5, 2.6, 2.8, 2.10, 2.11, 2.12, 2.17, 2.18

Topics Covered:
• Newton's second law in terms of momentum, Dynamics of a system of particles: total momentum and total external force, center of mass, motion of center of mass, conservation of momentum and its importance, impulse and the significance of interaction time.
  Relevant Sections in the Book: 3.1, 3.2, 3.3, 3.4
  Relevant Examples: 3.2, 3.6, 3.8 (no need to use the CoM coordinates), 3.10

Topics Covered:
• Work, Integrating the equation of motion in 1 dimension, Work-Energy theorem in 1 dim, Calculation of work for some forces: a) uniform gravitational field, b) linear restoring force, c) inverse square force (escape velocity)
• Integrating equation of motion in 3 dimensions, Work-Energy theorem, Work done by uniform and central forces, Conservative forces and potential energy, Total mechanical energy and its conservation, Potential in a uniform gravitational field, harmonic oscillator potential, gravitational potential, Shape of potential energy curve and stability.
  Relevant Sections in the Book: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.8, (recommended reading: 4.9, 4.10)
  Relevant Examples: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.8, 4.11, 4.12, 4.13,

Topics Covered:
• Angular momentum of a particle, Torque and the conservation of angular momentum, Central force motion and Kepler's law of equal areas, Angular momentum of an extended body and moment of inertia, Calculation of moment of inertia in some simple cases, The parallel axis theorem, Dynamics of pure rotation about an axis, kinetic energy of a rotating body, axis of gyration, The physical pendulum
  
• Motion Involving Both Translations and Rotations, analysis for angular momentum, torque and kinetic energy.
  Relevant Sections in the Book: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7
  Relevant Examples: 6.1, 6.2, 6.3, 6.5, 6.6, 6.7, 6.8, 6.9, 6.10, 6.14, 6.15, 6.16, 6.17

Topics covered:
• Transformations between reference frames, Galilean transformations and inertial frames, Uniformly accelerated systems and the equivalence principle, Physics in rotating coordinate systems, centrifugal and Coriolis forces, The case of the rotating earth, Foucault's pendulum
  Relevant Sections in the Book: 8.1, 8.2, 8.3, 8.4, 8.5
  Relevant Examples: 8.1, 8.2, 8.3, 8.6, 8.7, 8.8, 8.9, 8.11,

Topics covered:
• Review of simple harmonic motion, Damped harmonic oscillator, Forced harmonic oscillator, Forced damped harmonic oscillator, resonance and energy considerations
  Relevant Sections in the Book: 10.1, 10.2 (leave out the Q-factor), 10.3, 10.4
  Relevant Examples: 10.1, 10.3, 10.4, 10.5,

Topics covered:
• Galilean transformations and Galilean addition of velocities, Qualitative description of inconsistency with experiments and with the theory of electromagnetism (constancy of the speed of light), The postulates of Special Relativity, Derivation of Lorentz transformations.
  Relevant Sections in the Book: 11.1, 11.3,
  Relevant Examples: 11.1, 11.2

Topics covered:
• Implications of Lorentz Tansformations: observer dependence of simultaneity, Lorentz contraction, Time dilation, Relativistic transformation of velocity.
  Relevant Sections in the Book: 12.1, 12.2, 12.3, 12.4
  Relevant Examples: 12.1, 12.2, 12.3, 12.4, 12.5, 12.6, 12.7

Topics covered:
• Relativistic momentum and its conservation, the concept of velocity dependent mass, Relativistic kinetic energy,Total energy and mass-energy equivalence, energy-momentum relationship, the notion of massless particles.
  Relevant Sections in the Book: 13.1, 13.2, 13.3
  Relevant Examples: 13.2, 13.3, 13.5

Topics covered:
• Space intervals, Time intervals and Space-time intervals, Invariance of space-time intervals under Lorentz transformations, Types of Space-time intervals: space-like, time-like and light-like, The notion of causality and its invariance under Lorentz transformations, Space-time interval as a distance between two events in Minkowski space.
• Space-time diagrams, the light-cone and causality