PX15510 Classical Mechanics & Special Relativity
Introductory description
This module studies Newtonian mechanics and special relativity emphasizing the conservation laws inherent in the theory. These have a wider domain of applicability than just classical mechanics (for example they also apply in quantum mechanics). The module looks in particular at the mechanics of oscillations and of rotating bodies.
Einstein pointed out that Newton's laws were inconsistent with the theory of light waves: in mechanics objects only move relative to each other, whereas light appears to move relative to nothing at all (the vacuum). Einstein realised that Newtonian mechanics itself was the problem. He proposed that the laws of classical mechanics had to be consistent with just two postulates, namely that the speed of light is a constant and that all frames of reference are equivalent. These postulates forced Einstein to reject previous ideas of space and time and led directly to the special theory of relativity.
Module aims
To revise Alevel classical mechanics and to develop the theory using vector notation and calculus. To introduce special relativity. To cover material required for future physics modules.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Forces, interactions and Newton's Laws of Motion
Applying Newton's Laws  equilibrium, dynamics of particles, friction and dynamics of circular
motion
Work and kinetic energy.
Potential energy and energy conservation.
Conservation of momentum, elastic collisions, centre of mass
Rotation of rigid bodies  angular velocity and acceleration
Dynamics of rotational motion, conservation of angular momentum
Hooke's law, equation of motion for a mass attached to a spring on a frictionless plane. Solutions
for shm. Energy in shm. The pendulum, departures from shm for large amplitude. Complex
notation. Damping: critical and under/overdamping. Forced oscillations.
Motion as seen by different observers. Galilean Transformation of Velocities. Inertial frames of
reference
The Michelson Morley experiment. The universality of the speed of light. The meaning of
simultaneity.
Einstein's postulates: Lorentz transformation, Inverse Lorentz transformation and invariants.
Length Contraction and Time Dilation, Doppler Effect.
Einstein' energy and mass relation, energy and momentum of elementary particles.
Minkowski diagrams  graphical representation of past/present/future
Learning outcomes
By the end of the module, students should be able to:
 Solve F=dp/dt for a variety of cases
 Work with the concepts of kinetic and potential energy
 Recognise and solve the equations of forced and damped harmonic motion;
 Solve problems involving torque and angular momentum
 Explain the transformation between inertial frames of reference (Lorentz transformation) and work through illustrative problems
Indicative reading list
University Physics, Young and Freedman
View reading list on Talis Aspire
Interdisciplinary
Mechanics is inherently interdisciplinary. It uses mathematics to understand phenomena across physics, astronomy, engineering and living systems. It is about the use of calculus to describe motion and stability. Calculus is the mathematics coinvented by Newton to describe physical systems.
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.
Transferable skills
Analytical, communication, problemsolving, selfstudy
Study time
Type  Required 

Lectures  30 sessions of 1 hour (30%) 
Private study  70 hours (70%) 
Total  100 hours 
Private study description
Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for exam, practising on past exam papers
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group B
Weighting  Study time  

Inperson Examination  100%  
Answer 4 questions

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Core for:
 Year 1 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 1 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 1 of UPXAF300 Undergraduate Physics (BSc)
 Year 1 of UPXAF303 Undergraduate Physics (MPhys)
 Year 1 of UPXAF3F5 Undergraduate Physics with Astrophysics (BSc)
 Year 1 of UPXAF3FA Undergraduate Physics with Astrophysics (MPhys)
 Year 1 of UPXAF3N2 Undergraduate Physics with Business Studies
This module is Option list B for:
 Year 1 of UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 1 of UMAAG100 Undergraduate Mathematics (BSc)
 Year 1 of UMAAG103 Undergraduate Mathematics (MMath)
 Year 1 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 1 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 1 of UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
 Year 1 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 1 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
 Year 1 of UMAAG101 Undergraduate Mathematics with Intercalated Year