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Mechanics 1 (MATH 11009)

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Administrative Information

  1. Unit number and title: MATH 11009 Mechanics 1
  2. Level: C/4 (Honours)
  3. Credit point value: 10 credit points
  4. Year: 11/12
  5. First Given in this form: 2007
  6. Unit Organiser: Stephen Wiggins
  7. Lecturer: Stephen Wiggins
  8. Teaching block: 2
  9. Prerequisites: First teaching block of Linear Algebra and Geometry and Calculus 1

Unit aims

  • To introduce the basic principles and laws of classical mechanics.
  • To develop mathematical tools of kinematics and dynamics.
  • To illustrate the ideas of mechanics by applying them to certain classical problems.

 

General Description of the Unit

The development of the theory of mechanics is associated with many of the greatest names in mathematics, physics, and engineering. For example, problems in mechanics motivated Newton to invent calculus. Mechanics has developed continuously since then, and is now the foundation for all mathematical physics.

This unit is an introduction. It is designed to be accessible to motivated students with no previous exposure to mechanics. However, the material will progress fast beyond the A-levels, and the viewpoint based on calculus and linear algebra will be prevalent and essential. At the same time, the physics principles underlying not only mechanics, but the whole conceptual body of modern physics, from which such names as Galileo, Newton, and Einstein are inseparable, will be continuously emphasised throughout the course.

The unit begins with a brief discussion of the basic concepts of mechanics, such as the basic properties of space and time, inertial frame of reference and point particle. Newton's laws are introduced, followed by the laws of conservation of momentum, angular momentum, and energy, followed by the notion of work and conservative and conservative forces. Classical particle motion problems in one and two dimensions are studied in some detail.

 

Relation to Other Units

This unit is an essential part of the Year 1 core curriculum. It uses the methods of Linear Algebra and Geometry and Calculus 1 (and partially some methods systematically taught later in Calculus 2), as well as introduces some techniques of the analysis of Ordinary Differential Equations, taught in Year 2.

Teaching Methods

Lectures, homework, problem-solving and tutorials. Motivation and independent reading.

Learning Objectives

  • To create a solid foundation for understanding of basic principles of Mechanics and some of its classical problems.
  • To be able to use Calculus and Linear Algebra to approach these problems.
  • To open ways to further study of Applied Mathematics

Assessment Methods

The final assessment mark for Mechanics 1 is calculated from a standard rubric 1½ -hour written examination in May/June with two sections.

  • Section A (worth 40%) consists of 5 short mandatory questions.
  • Section B (worth 60%) consists of 3 long questions of which the best 2 will count.

Calculators are NOT permitted in this examination.

Award of Credit Points

To be awarded the credit points for this unit you must normally pass the unit, i.e. you must achieve an assessment mark of at least 40.

The assessment mark is calculated as described in the Assessment section above. Details of the university's common criteria for the award of credit points are set out in the Regulations and Code of Practice for Taught Programmes at http://www.bristol.ac.uk/esu/assessment/codeonline.html

Note that for this unit:

  • first year students are expected to attend all the relevant tutorials,
  • all students are expected to hand in attempts to the weekly exercises set.

Transferable Skills

Mechanics 1 is a pre-requisite for studying any further mathematical physics.  Even if you plan to further specialise in Pure Mathematics or Statistics, Mechanics will provide you with a rich source of mathematical techniques and  intuition for advancing in your studies.

 

Texts

There is no one standard text for the course. Online notes will be available on Blackboard. There are many excellent texts for this subject. The following books are suggested:

  1. An Introduction to Mechanics, D. Kleppner & Robert J. Kolenkow, McGraw-Hill, 1973
  2. Analytical Mechanics, G.R. Fowles & G.L. Cassiday, 6th ed. Saunders College Publishing (1993)
    This book covers the same ground as Kleppner and Kolenkow, except for special relativity.
  3. Mechanics (Berkeley Course), Charles Kittel, Walter D. Knight, & Malvin A. Ruderman.
    This is a good physics book with less emphasis on maths than Kleppner and Kolenkow.
  4. Mechanics P. Smith, and R.C. Smith. Chichester : Wiley, 1990.

Syllabus

  • Basic concepts of mechanics. Space, time, coordinates.
  • Trajectory, velocity and acceleration.
  • Newton's laws and the concept of force.
  • Equation of motion, examples in 1D.
  • Momentum. Impulse. Conservation of momentum.
  • Angular momentum, torque, pendulum.
  • Kinetic energy. Work done, power. Path-independence, potential energy, conservative forces.
  • Oscillations and phase plane analysis
  • Two-body problem and polar coordinates.