PHYS 2006 Classical Mechanics

Unit Coordinator: 
Dr Tim Freegarde 
Semester: 
1 

Prerequisites: 
First year physics core units 
Credit Points: 
15 

This is a core unit for all physics programmes 


Introduction
This course extends the methods and concepts of Newtonian mechanics introduced in
PHYS2015 Motion & Relativity, and
provides links to courses on oscillations and waves, quantum mechanics and condensed matter. Beginning with the
application of Newton's laws to systems of particles, it moves on to rotational motion, dynamical gravity (Kepler's
laws), motion in noninertial reference frames and systems of coupled oscillators, establishing throughout a rigorous
mathematical approach to reinforce and allow analysis of intuitive and everyday situations.
Learning Outcomes
After studying this course, students should be able to:
 discuss the linear motion of systems of particles (eg rocket motion)
 define angular momentum for a particle and a system
 define moment of inertia and use it in simple problems
 describe how steady precession occurs and work out the precession rate
 demonstrate that a spherically symmetric object acts gravitationally like a point with the same total mass located at the object's centre (providing you are outside the object)
 solve orbit problems using the conservation of angular momentum and total energy
 explain the origin of the Coriolis and centrifugal terms in the equation of motion in a rotating frame and solve problems in rotating frames
 identify normal modes for oscillating systems
 find normal modes for systems with many degrees of freedom by applying symmetry arguments and boundary conditions
Syllabus
 Linear motion of systems of particles: centre of mass; total external force equals rate of change of total momentum (internal forces cancel); examples (rocket motion)
 Angular motion: rotations, infinitesimal rotations, angular velocity vector; angular momentum, torque; angular momentum for a system of particles;
internal torques cancel for central internal forces; rigid bodies, rotation about a fixed axis, moment of inertia, parallel and perpendicular axis theorems, inertia tensor;
precession at steady rate, gyrocompass
 Gravitation and Kepler's laws: conservative forces; gravity; law of universal gravitation; gravitational attraction of spherically symmetric objects; twobody problem,
reduced mass, motion relative to centre of mass; orbits, Kepler's laws; energy considerations, effective potential
 Noninertial reference frames: fictitious forces, motion in a frame rotating about a fixed axis, centrifugal and Coriolis terms  apparent gravity, Coriolis deflection,
Foucault's pendulum, weather patterns
 Normal modes: coupled oscillators, normal modes; boundary conditions and Eigenfrequencies
Teaching and Learning Methods
Teaching is through a course of about 30 lectures, supplemented by exercises which are addressed weekly in separate problem classes.
Noncontact Hours
Students are expected to pursue six hours of independent study per week.
Assessment Methods
Weekly exercise sheets comprise 20% of the available marks for this course, with the remaining 80% allocated to the written examination
at the end of the semester. Section A of the exam paper will comprise five short, compulsory questions; section B will contain four
longer questions, of which only two should be answered.
Recommended Books and Course Materials
 G. R. Fowles & G. I. Cassiday  Analytical Mechanics, 7th edition, Brooks/Cole (2005)
ISBN 978 0534 408138
 T. L. Chow  Classical Mechanics, 2nd edition, CRC Press (2013)
ISBN 978 1466 569960
 A. P. French & M. G. Ebison  Introduction to Classical Mechanics, Springer (1986)
ISBN 978 0412 381409
 T. W. Kibble & F. H. Berkshire  Classical Mechanics, 5th edition, Imperial College Press (2004)
ISBN 978 1860 944352
 S. T. Thornton & J. B. Marion  Classical Dynamics of Particles and Systems, 5th edition, Brooks/Cole (2003)
ISBN 978 8131 518472
 D. Acheson  From Calculus to Chaos  an introduction to dynamics, O U P, Oxford (1998)
ISBN 978 0198 500773
 D. Morin  Introduction to Classical Mechanics, C U P, Cambridge (2008)
ISBN 978 0521 876223
 L. D. Landau & E. M. Lifshitz  Mechanics, 3rd edition, ButterworthHeinemann(1976)
ISBN 978 0750 628969
 M. L. Boas  Mathematical Methods in the Physical Sciences, Wiley, New York (1983) ISBN 978 0 471 19826 0
 R. P. Feynman Lectures in Physics, vol. 1, Basic Books (revised 2011) ISBN 978 0 465 02493 3

Lecture notes:
preface
chapter 1
chapter 2
chapter 3
chapter 4
chapter 5
chapter 6
chapter 7
appendix 1
Pythagoras
Rotations
Tensor MofI
Gyro instruments
Nutations
Rad/ang eqns
Rotating frames
Geostrophic wind
Ttrans symm
Avoided crossings
Lagrangian
Lecture slides:
set 1
PDF
set 2
PDF
set 3
PDF
set 4
PDF
set 5
PDF
set 6
PDF
set 7
PDF
set 8
PDF
set 9
PDF
set 10
PDF
QR
revision
Problem sheets:
Sheet 1
/ solns
Sheet 2
/ solns
Sheet 3
/ solns
Sheet 4
/ solns
Sheet 5
/ solns
Sheet 6
/ solns
Sheet 7
/ solns
Sheet 8
/ solns
Sheet 9
/ solns
Sheet 10
/ solns
Sheet 11
/ solns
Examinations:
2010
/ solns
2011
/ solns
2012
/ solns
2013
/ solns
2014
/ solns
2015
/ solns
2016
/ solns
report
2017
/ solns
report
2018
/ solns
report
2019
/ solns
report
2020
/ solns
report
Links:
Coriolis: billiards
Tippe top patent
Tippe top physics
Rattleback physics
Rattleback physics
Rattleback physics
Bicycle physics
Gyrocompass
Emmy Noether
 alt
Feynman: symmetry
