Module Identifier MP14010
Module Title DYNAMICS AND RELATIVITY
Co-ordinator Professor Geraint Vaughan
Semester Semester 1
Other staff Professor Keith Birkinshaw, Dr Sian A Jones
Pre-Requisite A-level Mathematics
Co-Requisite None
Mutually Exclusive PH14020
Course delivery Lecture   20 x 1-hour lectures
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours written examination  80%
Semester Assessment 2 assignments  20%
Supplementary Exam2 Hours written examination  100%

#### Learning outcomes

On completion of this module, students should be able to:
1. Describe the basic principles of Dynamics and Special Relativity;
2. Apply the basic principles to the description of classical and macroscopic phenomena;
3. Model problems in dynamics and special relativity with mathematical equations, apply basic solution techniques to these equations and interpret the results in the original physical context;
4. Provide models of planetary motion and explain how these are used for the prediction of events;
5. Describe the physics of rotational motion;
6. Solve numerical problems in linear and rotational dynamics and in special relativity.

#### Brief description

This module provides an introduction to the classical theory of dynamics and the theory of special relativity. The problems addressed in dynamics will involve classical kinematics, Newton's Laws, energy and momentum and rotational motion. The implications of the principles of special relativity for the concepts of space and time will also be studied. An emphasis will be placed on the solution of problems related to concepts and example sheets will include numerical exercises.

#### Aims

The module develops the principles and techniques of dynamics and relativity and is appropriate as a core module for honours degree schemes in Mathematics. It also prepares students for the more advanced approach to these topics developed in MP21010. MP14010 and MP21010 will take over the role of MA24510 in introducing students to basic concepts required for various Applied Mathematics modules?e.g. those in Hydrodynamics, Viscous flow and Partial Differential Equations.

#### Content

DYNAMICS
Kinematics: Newton's laws of motion; inertial frames; Galilean transformations; relativity principle of Newtonian mechanics; momentum and kinetic energy; collision processes; internal forces; centre-of-mass system.
Gravity and weight.
Universal gravitation: g and G; variation of g for terrestrial observer; planetary motion and artificial satellites.
Potential energy and gravitational fields.
Rotational motion: centripetal acceleration/force; moment of inertia; equation of motion; angular momentum; analogy between linear and rotational motion.
RELATIVITY
Introduction and discussion of the shortcomings of pre-relativistic physics, which lead to the simple postulates of Special Relativity, with spectacular results in our understanding of space and time. The Lorentz-Einstein transformations are derived from the postulates, leading to an understanding of time-dilation and Lorentz contraction.