Classical Mechanics and Relativity module (PH42008)

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Classical mechanics is the branch of physics concerned with understanding how objects move and interact with one another, from the motion of planets to everyday things like cars and bikes.  

After reviewing the fundamentals of classical mechanics, including Newton’s laws, energy, and rotational dynamics, you will study the alternative formulation of Lagrangian mechanics, where energy and momentum are used to describe the behaviour of systems rather than the Newtonian approach of force as a rate of change of momentum. You will discover how Newton used his force laws together with his law of universal gravitation to explain the physical meaning behind Kepler’s laws of planetary motion.  

The final weeks of the module are devoted to Einstein’s special theory of relativity, which explains how space and time are affected by the relative motion of observers. You will first learn why Galilean relativity failed and how special relativity was developed, then cover concepts such as the Lorentz transformation and the relativistic velocity-addition formula.  

Topics include: 

  • A review of classical mechanics 

  • Calculus of Variations 

  • The formulation of Lagrangian mechanics 

  • Planetary motion and effective potential 

  • Galilean Relativity and introduction to Special Relativity 

  • Lorentz transformation, time dilation, and length contraction 

  • Relativistic mechanics, four vectors, the invariant scalar product, and light cones 

  • Relativistic electromagnetism and tensors.