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Module MA22S4: Mechanics

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2013-14
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Dr. Brendan Redmond
Learning Outcomes
 
Module Content

Description:

This is a provisional syllabus.

  • Introduction

    Scalar and vector products, differentiation and integration of vectors, velocity and acceleration, Newton Laws.

  • Motion in Plane Polar Coordinates

    Derivation of velocity and acceleration in polar coordinates and applications to circular and elliptical motion of a particle.

  • Central Force Motion

    Equations of motion for a particle in a central force field, derivation of the orbit equation, conservation of angular momentum, potential energy, conservation of energy, solution of the orbit equation for different force fields, apsides and apsidal angles, calculation of maximum and minimum distance of a particle from the origin of a force, inverse square law of attraction and conic sections, properties of the ellipse. Planetary motion, Newton’s Universal Law of Gravitation, proof of Kepler’s Laws, examples involving calculating eccentricity, periodic time, velocity at aphelion and perihelion of planets and related problems.

  • Work and Energy

    Evaluation of work done by a force on a particle using line integrals, work as related to kinetic and potential energy, conservative forces, path independence, conservation of energy. Energy diagrams – use of energy diagrams to analyse the motion of a particle qualitatively, positions of stable and unstable equilibrium, small oscillations in a bound system.

  • Rotating Frames

    Non-inertial coordinate systems, velocity and acceleration in rotating systems, centrifugal and coriolis forces, derivation of the equation of motion for a particle moving in the vicinity of the rotating earth and related examples.

Textbooks

  1. An Introduction to Mechanics, Daniel Kleppner, Robert J. Kolenkow, McGraw-Hill (1973)

  2. Classical Mechanics, Tom W.B. Kibble, Frank H. Berkshire, Imperial College Press, 2004
  3. Theory and Problems of Theoretical Mechanics, Murray R. Spiegel, McGraw-Hill 1987
  4. Principles of Mechanics, John L. Synge, Byron A. Griffith, McGraw-Hill
 
Module Prerequisite
MA22S1
Assessment Detail
This module will be examined in a 2 hour examination in Trinity term. Continuous Assessment will contribute 10% to the final annual grade. Supplemental exams if required will consist of 100% exam.