Some of the material should be familiar to many of you, but you may find we look at it in more sophisticated ways. In particular, I will employ vectors and complex exponentials. I will try to highlight the importance of identifying symmetries to help with physical understanding. This should come up several times in the course.
The last topic in the mechanics section of Forces and Fields was gravitation. In this course we will return to gravity and derive the important result that the gravitational effect of a spherically symmetric object is the same as the effect of a point mass, with the same total mass, at its centre. We then discuss Kepler's laws of planetary motion. This was an early triumph for Newtonian mechanics. To link the observed effects of gravity on the Earth with the force governing celestial motion was really a stunning achievement.
We will actually begin, however, by considering the motion of systems of particles, allowing us to study such problems as rocket motion. We will then look at rotational dynamics, applying Newton's Laws to angular motion, encountering angular velocity, angular momentum and, for systems of particles, the moment of inertia. We will see some of the seemingly counterintuitive effects that arise in the motion of spinning objects.
We normally use inertial coordinate systems. However, the rotation of the Earth on its axis makes coordinate systems fixed to the Earth non-inertial. We'll work out the equation of motion in such a reference frame and see the effects that arise, discussing especially the Coriolis term.
Finally, we consider oscillations and waves. We'll revise the description of damped and forced harmonic oscillation and resonance. The techniques will then be extended to study systems of coupled oscillators. A one-dimensional system of masses joined by springs will furnish us with an introduction to waves in crystals. This simple system reveals a surprising amount of physics. This section of the course will lay the foundation for later courses on condensed matter.
<stefano@soton.ac.uk>