PX14812 Classical Mechanics & Special Relativity
Introductory description
By 1905, there was a successful theory (Newton's laws) describing the motion of massive bodies and there was a successful theory of light waves (Maxwell's equations of electromagnetism). But the two theories are inconsistent: in mechanics objects only move relative to each other, whereas light appears to move relative to nothing at all (the vacuum). Physicists (including Maxwell himself) had therefore assumed that there had to be some background 'ether', through which light propagated. But all attempts to detect this ether had failed. Einstein realised that there was nothing wrong with Maxwell's equations and that there was no need for an ether. 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.
This module studies Newtonian mechanics emphasizing the conservation laws inherent in the theory. These have a wider domain of applicability than classical mechanics (for example they also apply in quantum mechanics). It also looks at the classical mechanics of oscillations and of rotating bodies. It then explains why the failure to find the ether was such an important experimental result and how Einstein constructed his theory of special relativity. The module covers some of the consequences of the theory for classical mechanics and some of the predictions it makes, including: the relation between mass and energy, lengthcontraction, timedilation and the twin paradox.
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
This module is taken by students within Mathematical Sciences (mainly Maths and Physics). Mechanics is largely 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 (25%) 
Private study  90 hours (75%) 
Total  120 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 B1
Weighting  Study time  

3 hour online examination (Summer)  100%  
Answer 4 questions

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Core for:
 Year 1 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 1 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 1 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 1 of UPXAF304 Undergraduate Physics (BSc MPhys)
 Year 1 of UPXAF300 Undergraduate Physics (BSc)
 Year 1 of UPXAF303 Undergraduate Physics (MPhys)
 Year 1 of UPXAF3N1 Undergraduate Physics and Business Studies
 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 Optional for:
 Year 1 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 1 of USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 1 of USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
This module is Option list B for:
 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 UMAAGV17 Undergraduate Mathematics and Philosophy
 Year 1 of UMAAGV18 Undergraduate Mathematics and Philosophy with Intercalated Year
 Year 1 of UMAAG101 Undergraduate Mathematics with Intercalated Year