MA1300: Mechanics I

School Cardiff School of Mathematics
Department Code MATHS
Module Code MA1300
External Subject Code G121
Number of Credits 10
Level L4
Language of Delivery English
Module Leader Dr David Binding
Semester Spring Semester
Academic Year 2014/5

Outline Description of Module

Classical continuum mechanics is a branch of mechanics, physics, and mathematics concerned with the behaviour of physical bodies which are either moving or at rest under the action of forces. This lecture based module focuses on basic continuum mechanics concepts and in particular on Newton's laws of dynamics, which are presented using modern mathematical tools and are applied to solve a number of mechanical problems taken from the physical world. 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 using polar coordinates;
  • 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 predict 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, and to prove Kepler’s laws of planetary motion.

How the module will be delivered

27 - 50 minute lectures

5 - 50 minute tutorial classes

Some handouts will be provided in hard copy or via Learning Central, but students will be expected to take notes of lectures.

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;

Use of polar coordinates and analytic geometry of conics.

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 in-course element of summative assessment is based on selected homework exercises.

The major component of summative assessment is the written examination at the end of the module.  This gives 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 85 Mechanics I 2
Written Assessment 15 Coursework N/A

Syllabus content

  • Particle Kinematics
    • Motion of a particle in space and time
    • Use of polar coordinates, circular motion
  • Newton's Laws of Dynamics
    • Galilean relativity
    • Gravitational law, satellites
    • Resisted motion, projectiles, frictional contact
  • Linear Oscillations
    • Free and forced linear oscillations, simple seismograph
    • Simple oscillatory systems with two degrees of freedom
  • Energy Conservation
    • Mechanical energy
    • Energy conservation in rectilinear motion
    • Motion and equilibrium positions of a particle in a conservative force field
  • Orbits in Central Field
    • The one-body problem, conservation of angular momentum
    • The path equation
    • Inverse square field, analytical geometry of conics
    • Planetary orbits, Kepler’s laws of planetary motion

Essential Reading and Resource List

Please see Background Reading List for an indicative list.

Background Reading and Resource List

Classical Mechanics, Gregory, R. D., Cambridge University Press, 2006

Theoretical Mechanics, Love, A. E. H., Cambridge University Press, 1906

A First Course in Mechanics, Lunn, M., Reprinted, Oxford University Press, 2009


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