PHY1021 Vector Mechanics

2011-2012

Code: PHY1021
Level: 1
Title: Vector Mechanics
Instructors: Dr S. Foteinopoulou
CATS Credit Value: 15
ECTS Credit Value: 7.5
Pre-requisites: N/A
Co-requisites: N/A
Duration: T1:01-11
Availability: unrestricted
Background Assumed: -

Total Student Study Time

150 hours, to include: 22×1-hour lectures; 44 hours directed self-study; 9 hours of problems class support; 3 hours of tutorial support; 72 hours private study.

Aims

Our interest in mechanics arises from 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 that will apply the principles of mechanics to the solution of more complex problems.

Intended Learning Outcomes

Students will be able to:

1. Module Specific Skills:
   1. recognise and describe the forces that are relevant in a given mechanics situation;
   2. describe the origin of and relationship between these forces, and to describe what their consequences will be;
   3. solve a range of mechanics problems as defined by the syllabus below, and by examples given in the lectures and worksheets.
2. Discipline Specific Skills:
   1. apply general problem-solving strategies not only to mechanics but also to the solution of other physics problems;
   2. apply their knowledge of mechanics in a wide range of other physics modules.
3. Personal Transferable Skills:
   1. undertake guided self-study successfully;
   2. meet deadlines for completion of work for problems classes and develop appropriate time-management strategies.

Learning / Teaching Methods

Lectures, e-Learning resources (ELE PHY1021), and problems classes.

Assessment and Assignments

Contribution	Assessment/Assignment	Size (duration/length)	When
10%	Problem Sets	7×2hrs	Weekly
15%	Mid-term Test 1	30 minutes	Week T1:04
15%	Mid-term Test 2	30 minutes	Week T1:08
60%	Final examination	120 minutes	Week T2:00
Formative	Guided self-study	5×6-hour packages	Fortnightly

Syllabus Plan and Content

1. Introduction and Background
   Brief historical survey; units.
2. Vectors
   Definition, addition, subtraction, dot-product, cross-product, components; scalar and vector triple products and their physical interpretations; equation of a straight line; equation of a plane; parametric specification of points on lines and planes; intersection of a line and a plane; use of the dot and cross products; the time derivative of a vector.
3. Motion
   velocity and acceleration (vector formalism); linear and circular motion; centripetal acceleration; relative motion, projectiles
4. Forces
   Types of forces; units and dimensions; vector addition of forces.
5. Newton's Laws of Motion
   The first law - inertial frames of reference; the second Law - force mass and weight; the third law.
6. Systems of Particles and Rigid Bodies
   Center of mass, Newton's laws for systems of particles and rigid bodies; moments of inertia; products of inertia.
7. Torque or Moment of Force
   Definitions, Newton's second law for rotational motion.
8. Equilibrium
   Conditions of equilibrium and their application to specific examples.
9. Kinetic Energy
   Kinetic energy of: a particle, a system of particles, rigid bodies (rotation around fixed axis), rigid bodies (rotation around moving axis).
10. Work
    Work done by a constant force; work done by a variable force; work kinetic energy theorem; power.
11. Conservative Forces and Conservation of Energy
    Conservative forces in one and three dimensions; examples of potential theory (elastic energy, interatomic and Yukawa potential), energy diagrams, force and potential energy.
12. Motion in Constant Uniform Gravitational Field
    Circular motion in a vertical circle; rolling without slipping; examples.
13. Momentum, Impulse and Newton's Second Law
    Linear momentum and impulse; angular momentum; conservation of linear and angular momentum; center of percussion; gyroscopes; rocket motion (variable mass problem).
14. Collisions
    Elastic and inelastic collisions.
15. Introduction to Relativity
    The Special Theory of Relativity; relativistic dynamics: Lorentz transformations, the Minkowskian space and the light-cone, the energy-momentum relationship and relativistic collisions.

Core Text

Young H.D. and Freedman R.A. (2011), University Physics (with Modern Physics) (13^th edition), Addison-Wesley, ISBN 978-1-292-02063-1 (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 (4^th edition), Harcourt Brace and Co (UL: 531.11 MAR)
Spiegel M.R. and Lipschutz S. (2009), Schaum's Outline of Vector Analysis (2^nd edition), McGraw-Hill, ISBN 9780-071615-45-7 (UL: 515.63)

IOP Accreditation Compliance Checklist

• CM-01: Newton's laws and conservation laws including rotation.
• SR-01: Lorentz transformations.
• SR-02: The energy-momentum relationship.

Formative Mechanisms

Students monitor their own progress by attempting the problem sets which will be discussed in classes. Students who need additional guidance are encouraged to discuss the matter with the lecturer or their tutor.

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.