The University of Southampton
Courses

# PHYS2006 Classical Mechanics

## Module Overview

Beginning with a review of Newton's Laws applied to systems of particles, the course moves on to rotational motion, dynamical gravity (Kepler's Laws) and motion in non-inertial reference frames. Systems of coupled oscillators are studied.

### Aims and Objectives

#### Module Aims

The aim of this course is to continue with and consolidate the Mechanics studied in PHYS1015 Motion & Relativity. Its ideas link with other courses on oscillations and waves, quantum mechanics and condensed matter.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Discuss the linear motion of systems of particles (e.g. rocket motion)
• Define angular momentum for a particle and a system
• Define moment of inertia and use it in simple problems
• Explain the origin of the Coriolis and centrifugal terms in the equation of motion in a rotating frame
##### Cognitive Skills

Having successfully completed this module you will be able to:

• Describe how steady precession occurs and work out the precession rate
##### Disciplinary Specific Learning Outcomes

Having successfully completed this module you will be able to:

• Solve orbit problems using the conservation of angular momentum and total energy
• Solve problems in rotating frames identify normal modes for oscillating systems
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Find normal modes for systems with many degrees of freedom by applying symmetry arguments and boundary conditions.

### Syllabus

The numbers of lectures indicated for each section are approximate. Linear motion of systems of particles [4 lectures] - Centre of mass - Total external force equals rate of change of total momentum (internal forces cancel) - Examples (rocket motion). Angular motion [6 lectures] - 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 mentioned - Precession (simple treatment: steady precession rate worked out), gyrocompass described. Gravitation and Kepler's Laws [6 lectures] - Conservative forces - Gravity - Law of universal gravitation - Gravitational attraction of spherically symmetric objects - Two-body problem, reduced mass, motion relative to centre of mass - Orbits, Kepler's laws - Energy considerations, effective potential. Non-inertial reference frames [4 lectures] - 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 [4 lectures] - Coupled oscillators, normal modes - Boundary conditions and Eigen Frequencies. Towards the end of the course, some lectures are normally devoted to revision.

### Learning and Teaching

TypeHours
Preparation for scheduled sessions18
Revision10
Tutorial12
Lecture36
Follow-up work18
Total study time150

T W B Kibble & F H Berkshire (2004). Classical Mechanics.

J B Marion and S T Thornton (1995). Classical Dynamics of Particles and Systems.

T W B Kibble (1973). Classical Mechanics.

K F Riley and M P Hobson (2011). Foundation Mathematics for the Physical Sciences.

G R Fowles and G I Cassiday (1993). Analytical Mechanics.

A P French (1971). Vibrations and Waves.

K F Riley and M P Hobson (2011). Essential Mathematical Methods for the Physical Sciences.

PA Tipler (2004). Physics for Scientists and Engineers.

TL Chow (1995). Classical Mechanics.

D Acheson (1997). From Calculus to Chaos: an Introduction to Dynamics.

A P French and M G Ebison (1986). Introduction to Classical Mechanics.

### Assessment

#### Assessment Strategy

Problem sheets consist of four questions, each week only two will be marked, picked at random. Weekly course work will be set and assessed in the normal way, but only the best ‘n-2’ attempts will contribute to the final coursework mark. Here n is the number of course work items issued during that Semester. As an example, if you are set 10 sets of course work across a Semester, the best 8 of those will be counted. In an instance where a student may miss submitting one or two sets of course work, those sets will not be counted. Students will, however, still be required to submit Self Certification forms on time for all excused absences, as you may ultimately end up missing 3+ sets of course work through illness, for example. The submitted Self Certification forms may be considered as evidence for potential Special Considerations requests. In the event that a third (or higher) set of course work is missed, students will be required to go through the Special Considerations procedures in order to request mitigation for that set. Please note that documentary evidence will normally be required before these can be considered.

#### Summative

MethodPercentage contribution
Exam  (2 hours) 80%
Problem Sheets 20%

#### Referral

MethodPercentage contribution
Coursework marks carried forward %
Exam %

#### Repeat Information

Repeat type: Internal & External