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

#### 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
##### 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.
##### 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
##### Cognitive Skills

Having successfully completed this module you will be able to:

• Describe how steady precession occurs and work out the precession rate

### 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.

### Learning and Teaching

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

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

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

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

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

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

TL Chow (1995). Classical Mechanics.

A P French (1971). Vibrations and Waves.

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

Tim Freegarde (2012). Introduction to the Physics of Waves.

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

### 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, where 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 misses submission of one or two sets of course work, these sets will not be counted. Students will, however, still be required to submit Self Certification forms on time for all excused absences, as they 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
Continuous Assessment 20%
Final Assessment  80%

#### Repeat

MethodPercentage contribution

#### Referral

MethodPercentage contribution