Aims
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.
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.
Assessment methods
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.
| Method | Hours | Percentage contribution |
|---|
| Problem Sheets | - | 20% |
| Exam | 2 hours | 80% |
Referral Method: See notes below
By examination, the final mark will be calculated both with and without the coursework assessment mark carried forward, and the higher result taken.