Course Details in 2023/24 Session

Module Title	LC Special Relativity and Dynamical Systems
School	Physics and Astronomy
Department	Physics & Astronomy
Module Code	03 33962
Module Lead	Rob Smith & Dimitri Gangardt
Level	Certificate Level
Credits	10
Semester	Semester 1
Pre-requisites
Co-requisites
Restrictions	None
Contact Hours	Lecture-24 hours Tutorial-11 hours Guided independent study-65 hours Total: 100 hours
Exclusions
Description	This module provides a detailed mathematical treatment of topics in mechanics suitable for theoretical physics students. The first half of the module develops Einstein’s theory of special relativity, which is necessary to describe bodies moving at speeds close to that of light. The discovery that the speed of light is the same in all inertial frames means that Newton’s laws of motion and our ideas of space and time need to be modified. We derive the Lorentz transformations, which allow observers in different frames to reconcile their observations, and apply these to describe various phenomena. The second half of the module concerns the application of Newtonian mechanics to more complicated systems, such as rigid bodies and fluids, and shows how the equations describing such systems are derived from Newton’s laws of motion. These ideas and equations are then applied to problems such as truss bridges, hanging chains, floating bodies, and fluid flow in a pipe.
Learning Outcomes	By the end of the module students should be able to: Derive and use Lorentz transformations to translate events between inertial frames. Understand and calculate time dilation, length contraction, and the Twins Paradox. Use relativistic energy-momentum, and its invariant, to solve simple problems in relativistic kinematics. Understand how Newtonian mechanics emerges as the low velocity limit of special relativity. Derive and use the force and torque balance equations for statics problems in rigid body systems. Formulate and solve equations for projectile motion in simple systems. Derive and use Archimedes’ principle to describe bodies floating and sinking in fluids. Derive and use Bernoulli’s equation for incompressible, inviscid fluid flow. Understand (but not derive the detailed mathematics of) viscosity and advection in a fluid.
Assessment	33962-01 : Examination : Exam (Centrally Timetabled) - Written Unseen (80%) 33962-02 : Assessed problems : Coursework (20%)
Assessment Methods & Exceptions	Coursework (20%); 1.5 hour Examination (80%)
Other
Reading List