Classical Mechanics

Learning Outcomes

Knowledge and Understanding

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

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

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

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.

Cognitive Skills

Having successfully completed this module you will be able to:

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

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.

Resources & Reading list

Internet Resources

Online Materials.

Textbooks

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

TL Chow (1995). Classical Mechanics. John Wiley.

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.

A P French (1971). Vibrations and Waves. MIT Introductory Physics Series, Van Nostrand Reinhold.

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

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

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

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

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

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

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.

Repeat Information

Repeat type: Internal & External