Module Identifier MP14010
Module Title DYNAMICS AND RELATIVITY
Co-ordinator Dr Eleri Pryse
Semester Semester 1
Other staff Professor Keith Birkinshaw
Pre-Requisite A-level Mathematics
Co-Requisite None
Course delivery Lecture   20 x 1-hour sessions of lectures and example classes
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours written examination  70%
Semester Assessment Course Work: 2 Example sheets.  30%
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. 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;
3. 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 motion under gravity. 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 and example sheets will include numerical exercises.

#### Aims

The module develops the principles and techniques of dynamics and relativity, with emphasis on problem solving, 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.

#### Content

VECTORS
Recap: scalar and vector quantities, position vector, vector components, unit vectors, scalar and vectors products.

DYNAMICS
Kinematics: constant acceleration, projectile motion
Newton's Law of Motion: momentum, weight, contact forces on solids, friction, circular motion and centripetal face, drag force.
Work and Energy: work done by face, kinetic energy, power, conservative force, potential energy, conservation of mechanical energy.
Conservation of Momentum: centre-of-mass, collisions, coefficient of restitution, rocket propulsion
Gravity: Kepler's Laws, Newton's Law of Gravity, gravitational potential energy

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.

#### Module Skills

 Problem_solving Problem solving skills are developed throughout this module and tested in assignments and in the written examination.