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This course will explore further some of the topics you met last semester in PC 1101 Dynamics and PC 1111 Relativity. It will also give you an opportunity to apply techniques from the mathematical physics courses (especially PC 1171 Vectors, fields and matrices) to more challenging physical problems.
Symmetry principles in physics will be introduced and the idea of component vectors in ordinary space will be extended to space-time four-vectors. These provide an elegant and powerful way to represent the results of Special Relativity. We shall use the energy-momentum four-vector in particular to solve problems in relativistic kinematics.
The rest of the course will make use of vector methods in the context of nonrelativistic dynamics. We shall use these methods to look at motion from the the viewpoint of a rotating frame of reference. This will allow us to describe such motion in terms of inertial forces (centrifugal and Coriolis).These will be illustrated with examples including Foucault's pendulum and the weather.
Newton's theory of gravitation will be studied in more detail, focussing on cases involving motion under the influence of a central force. We shall derive the general form of orbits for an inverse-square-law force and so arrive at Kepler's Laws. We shall apply these to problems of planetary motion and space travel. We shall also look at the role of gravity in other astronomical contexts, such as the tides and the expansion of the universe.
The vector nature of angular momentum and angular velocity will be explored and illustrated with rotating systems such as gyroscopes. The moment-of-inertia tensor will be introduced to relate the angular velocity and angular momentum of a rigid body. We shall examine the significance of the principal moments of inertia and the principal axes for freely rotating bodies. We shall use eigenvalue techniques to find the principal moments and apply these to solve problems in rotational dynamics.
For the topics to be covered see the syllabus or go direct to the course contents page. See also the course description taken from the Blue Book entry on this course.
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Mike Birse
5th April 2001