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PHY1105 Relativity I and Vectors

2007-2008

Code: PHY1105
Title: Relativity I and Vectors
Instructors: Prof. Bill Barnes
CATS credits: 10
ECTS credits: 5
Availability: unrestricted
Level: 1
Pre-requisites: N/A
Co-requisites: N/A
Background Assumed: AS level Physics or equivalent
Duration: Semester I
Directed Study Time: 22 lectures
Private Study Time: 66 hours
Assessment Tasks Time: 12 hours
Observation report: 2003/04 PGP

Aims

Our interest in mechanics is rooted in its general applicability to a vast number of familiar phenomena. This module provides meaningful and easily visualizable problems which allow development of the skills of problem solving, required in all the fields of physics. It provides the necessary background to later modules including PHY2007 and PHY3135 which extend the principles of mechanics to the solution of more complex problems.

This module also introduces the special theory of relativity. This provides an early opportunity to become aware of the far-reaching consequences of the theory with regard to our understanding of mass, length and time, and a step towards later modules in relativity, cosmology, and nuclear and high-energy physics.

Intended Learning Outcomes

Students will be able to:

  • recognise and describe what forces are relevant in a given mechanics situation,
  • describe the origin of and relationship between these forces, and to describe what their consequences will be,
  • solve a range of mechanics problems as defined by the syllabus below, and by examples given in the lectures and worksheets,
  • describe the ways in which special relativity leads us to a re-evaluation of the concepts of space, time, mass and energy,
  • recognise those mechanics problems that are likely to require special relativity in their explanation,
  • solve a range of special-relativity-based mechanics problems as defined by the syllabus below and by examples given in the lectures and worksheets.

Transferable Skills

  • General problem-solving strategies applicable not only to mechanics but also to the solution of other physics problems,
  • An understanding of mechanics applicable to a wide range of other physics modules,
  • Students are required to meet deadlines for completion of work for problems classes and must therefore develop appropriate time-management strategies.

Learning and Teaching Methods

Lectures, worksheet assignments, tutorials and problems classes, on-line teaching resources.

Assignments

Worksheets are handed out after every lecture. Problem assignments are issued for problem classes.

Assessment

Problems-class assignments (10%), two mid-semester tests (40%) and one 90-minute examination (50%).

Syllabus Plan and Content

Note: references in square brackets refer to the recommended text.

Vector Mechanics (15 lectures)

  1. Forces [Y&F 4.1]
    1. Types of forces
    2. Units and dimensions
    3. Vector addition of forces
    4. Newton's Laws of Motion [Y&F 4.2-4.6]
      1. Newton's 1st law; Inertial frames of reference
      2. Newton's 2nd Law; Mass and weight
      3. Newton's 3rd law
  2. Torque or Moment of Force [Y&F 10.1-10.2, 11.1-11.3]
    1. Definitions (Y10.1]
    2. Rigid body in a constant gravitational field
    3. Equilibrium against rotation
  3. Work [Y&F 6.1-6.5]
    1. Work done by a constant force
    2. Work done by a variable force
    3. Work and kinetic energy
    4. Power
  4. Conservative Forces and Conservation of Energy
    1. For one-dimensional motion [Y&F 7.4]
    2. Conservative forces in three dimensions [Y&F 7.5]
    3. Examples of potential theory
  5. Constant gravitational force [Y&F 7.2]
  6. Elastic energy [Y&F 7.3]
  7. Force and Potential Energy
    1. The relationship between force and potential [Y&F 7.6]
    2. Energy diagrams
      1. Interatomic potential [Y&F 44.2]
      2. Electrostatic potential energy [Y&F 24.2]
      3. Nuclear potential [Y&F 45.3]
  8. Gravitation [Y&F 12.1-12.8]
    1. The force of gravity
    2. Gravitational potential energy
    3. The motion of satellites
    4. The motion of the planets
    5. Spherical mass distributions
    6. Apparent weight and the Earth's rotation
  9. Circular motion [Y&F 5.5]
    1. Centripetal acceleration
    2. Motion in a vertical circle
  10. Using vectors [Y&F 1.11]
    1. The scalar product
    2. The cross product
  11. Momentum and impulse [Y&F 8.1-8.3]
    1. The relationship between momentum, kinetic energy and impulse
    2. Conservation of momentum
  12. Collisions
    1. Inelastic and elastic collisions [Y&F 8.4-8.6]
    2. Frames of reference
  13. Vectors
    1. Equation of a straight line
    2. Equation of a plane
    3. Intersection of a line and a plane
    4. Using the dot and cross products
  14. Rocket motion
    1. Variable-mass problems [Y&F 8.7]
    2. The gravitational sling-shot [Y&F 8.5]
  15. Projectiles
    1. From Newton's law to useful equations
    2. Range of projectiles

Relativity (7 lectures)

  1. Introduction to Relativity [Y&F pp 1072-1079]
    1. The principle of relativity
    2. Review of the Galilean transformations
    3. Problems with Newtonian mechanics
    4. Experiments on the constancy of the speed of light
  2. The Special Theory of Relativity [Y&F Ch. 39]
    1. The Lorentz transformations
    2. Time dilation and the clock paradox
    3. Lorentz contraction
    4. The concept of invariance: invariance of the interval
    5. Simple space-time diagrams [Y&F pp 1087-1092]
  3. Relativistic Dynamics [Y&F Ch. 39]
    1. Velocity transformations
    2. Momentum and energy
    3. Conservation of momentum
    4. Kinetic energy
    5. Rest mass and energy
    6. Examples of the use of E = mc2

Core Text

Young H.D. and Freedman R.A. (2000), University Physics (with Modern Physics) (10th edition), Addison-Wesley, ISBN 0-201-60336-5 (UL: 530 YOU)

Supplementary Text(s)

Feynman R.P., Leighton R.B. and Sands M. (1963), Lectures on Physics, Vol. I, Addison-Wesley, ISBN 0-201-02116-1 (UL: 530 FEY/X)
Marion J.B. and Thornton S.T. (1995), Classical Dynamics of Particles and Systems (4th edition), Harcourt Brace and Co (UL: 531.11 MAR)
McComb W.D (1999), Dynamics and Relativity, Oxford University Press, ISBN 0-198-50112-9 (UL: In processing)

Formative Mechanisms

This module is supported by problems classes and tutorials. Students are able to monitor their own progress by attempting problems sheets provided in the lectures. The graded mid-semester test scripts are discussed by tutors. Students with specific problems should first approach their tutor, and if the problem is not resolved, the lecturer.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.

                                                                                                                                                                                                                                                                       
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