MA1301: Classical Mechanics

School Cardiff School of Mathematics
Department Code MATHS
Module Code MA1301
External Subject Code 100400
Number of Credits 10
Level L4
Language of Delivery English
Module Leader Dr Usama Kadri
Semester Spring Semester
Academic Year 2019/0

Outline Description of Module

Mechanics is a scientific discipline that is concerned with the characteristics and behaviour of a substance or physical objects when displaced, or experienced a force.

There are two broad objectives of the module. The first is to bridge between the physical world and the mathematical derivations we employ to better understand how things work, in classical mechanics. The second, is to develop critical thinking.

The module is strongly recommended to all those who intend to pursue further study in applied mathematics, as well as to those interested in the roots of mathematics.

Free Standing Module Requirements:  A pass in A-Level Mathematics of at least Grade A

On completion of the module a student should be able to

On completion of the module the students will be familiar with the laws of motion, including circular and planetary motion. They will know how forces are used and be introduced to the concepts of energy and angular momentum and their conservation laws. The key feature of the module is that every new concept and technique is reinforced by fully worked examples, so that, at the end of the module, the students will be able to:

  • Solve simple problems in particle kinematics involving the motion of a particle in space and time, including circular motion;

  • Apply Newton’s laws of dynamics and the law of gravitation to determine the motion of a particle under the action of forces, including motion through a resisting medium, and simple oscillatory motions;
  • Apply the concept of mechanical energy and its conservation law to calculate the motion and equilibrium positions of a particle in a conservative force field;
  • Use conservation of angular momentum and energy to determine the orbit of a particle in a central force field.

How the module will be delivered

27 fifty-minute lectures

5 fifty-minute tutorial classes

Home reading and assignments.

Students are also expected to undertake at least 50 hours private study including preparation of worked solutions for tutorial classes.

Skills that will be practised and developed

Modelling of a physical system by differential equations;

Use of units of measurement;

Solving elementary differential equations;

Use of vector algebra and calculus;

How the module will be assessed

Formative assessment is carried out by means of regular tutorial exercises.  Feedback to students on their solutions and their progress towards learning outcomes is provided by the marking of tutorial exercises.  

The summative assessment is made up of coursework (10%) and the written examination at the end of the module.  These assessments give students the opportunity to demonstrate their overall achievement of learning outcomes.  It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.

The examination paper has two sections of equal weight.  Section A contains a number of compulsory questions of variable length but normally short.  Section B has a choice of two from three equally weighted questions.

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Spring Semester 90 Classical Mechanics 2
Written Assessment 10 Coursework N/A

Syllabus content

  1. Units and dimensions (self-study)
  2. Introduction to kinematics
  3. Vectors: dot & cross products
  4. The motion of projectiles: 3D kinematics
  5. Uniform circular motion: centripetal forces & perceived gravity.
  6. Newton’s first, second, and third laws
  7. Weight, perceived gravity, and weightlessness
  8. Frictional forces
  9. Hooke’s law: simple harmonic oscillator
  10. Work, energy, and universal gravitation
  11. Resistive forces: viscosity, air drag
  12. Potential energy and harmonic oscillators
  13. Elastic and Inelastic Collisions
  14. Momentum of individual objects
  15. Rotating rigid bodies & angular momentum
  16. Orbits and escape velocity
  17. Conservation of Momentum & centre of mass
  18. Torque and physical pendulum
  19. Rolling motion, gyroscopes
  20. Static equilibrium, stability: rope walker
  21. Gases and incompressible liquids
  22. Hydrostatics, Archimedes’ principle, and fluid dynamics
  23. Harmonics & resonance

Essential Reading and Resource List

An interactive version of this list is now available via our new reading list software: https://whelf-cardiff.alma.exlibrisgroup.com/leganto/public/44WHELF_CAR/lists/6034768990002420?auth=SAML


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