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.
Linked modules
Pre-requisites: PHYS1011 AND PHYS1013 AND PHYS1015 AND MATH1007 AND (MATH1006 or MATH1008)
Aims and Objectives
Learning Outcomes
Disciplinary Specific Learning Outcomes
Having successfully completed this module you will be able to:
- Solve problems in rotating frames identify normal modes for oscillating systems
- Solve orbit problems using the conservation of angular momentum and total energy
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Define angular momentum for a particle and a system
- Define moment of inertia and use it in simple problems
- Discuss the linear motion of systems of particles (e.g. rocket motion)
- 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
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.
Learning and Teaching
| Type | Hours |
|---|---|
| Completion of assessment task | 10 |
| Wider reading or practice | 46 |
| Follow-up work | 18 |
| Preparation for scheduled sessions | 18 |
| Revision | 10 |
| Lecture | 36 |
| Tutorial | 12 |
| Total study time | 150 |
Resources & Reading list
Internet Resources
Textbooks
TL Chow (1995). Classical Mechanics. John Wiley.
J B Marion and S T Thornton (1995). Classical Dynamics of Particles and Systems. Saunders College Publishing.
D Acheson (1997). From Calculus to Chaos: an Introduction to Dynamics. Oxford University Press.
K F Riley and M P Hobson (2011). Foundation Mathematics for the Physical Sciences. Cambridge University Press.
Tim Freegarde (2012). Introduction to the Physics of Waves. Cambridge: Cambridge University Press.
T W B Kibble & F H Berkshire (2004). Classical Mechanics. World Scientific Publishing.
A P French and M G Ebison (1986). Introduction to Classical Mechanics. Van Nostrand Reinhold.
A P French (1971). Vibrations and Waves. MIT Introductory Physics Series, Van Nostrand Reinhold.
G R Fowles and G I Cassiday (1993). Analytical Mechanics. Saunders College Publishing.
K F Riley and M P Hobson (2011). Essential Mathematical Methods for the Physical Sciences. Cambridge University Press.
Assessment
Assessment strategy
Course work worth 20% of the module mark will be set and assessed in the normal way. In the event that a course work is missed, students will be required to go through the Special Considerations procedures in order to request mitigation for that piece of course work. Please note that documentary evidence will normally be required before these can be considered.
The final exam is worth 80% of the module mark.
Referral Method: By examination, the final mark will be calculated both with and without the coursework assessment mark carried forward, and the higher result taken.
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Examination | 80% |
| Problem Sheets | 20% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Examination | 80% |
| Coursework marks carried forward | 20% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Examination | 80% |
| Coursework marks carried forward | 20% |
Repeat Information
Repeat type: Internal & External