Contents

• Background information
• Course information
• Reading List
• Syllabus
• Problem Sheets
• Previous Exam Papers and Model Solutions
• Computer Demonstrations
• Standard departmental course profile

Announcements

• Isaac Newton's `Principia'. You cannot afford not to read it (at least) once in a lifetime ...

Notes and Slides

Supplementary Material

• For mathematical bits and bobs, a good reference is MathWorld, (e.g., type "cross product" in the search box), courtesy from Wolfram.
• Relation between tri-dimensional Cartesian and polar coordinates: look here.
• The conservation of angular momentum is a law of physics that states the total angular momentum of a rotating object with no outside force remains constant regardless of changes within the system (see Sect. 2.1 of the notes). An example of this principle occurs when a skater pulls his or her arms/legs inward during a spin (changing the mass distribution to one nearer the rotation axis, thereby reducing the "moment of inertia (MoI)," and speeds up (increasing the skater's spin). Because the MoI goes down, the spin rate must increase to keep the total angular momentum of the system unchanged. See a video illustrating this. Try it yourself on a swivelling/rotating chair (you can hold two heavy books in your hands to appreciate more the effect).
• How a cat lands on its feet. A free-falling cat cannot alter its total angular momentum. Nonetheless, by swinging its tail and twisting its body to alter its moment of inertia, the cat can manage to alter its orientation
• Interested in the MoI of solid objects ? Here are some examples.
• A visualisation of the computation of the MoI of a solid cylinder can be found here.
• Demo of a spinning top. Look this one up too, it will help visualising the motion.
• A note on various definitions (all equivalent) of conservative force can be found here.
• Here is the explicit derivation of the eqs. (3.2) of the lecture notes.
• Here is the explicit derivation of the radial and angular equations of motion in page 27 of the lecture notes.
• Here is the explicit derivation of the solution to the radial equation of motion in page 31 of the lecture notes.
• Take a look here for animated Kepler's laws.
• Use either this or this applet to generate your own orbit, including a change of observer frame, and visualise all the dynamical parameters.
• Puzzled by the `effective gravitational potential' ? See for yourself at this website what it all means and play around with the `orbit applet'.
• Movie (for RealPlayer/MediaPlayer or QuickTime) of a ball rolling across the surface of a rotating merry-go-round (see Fig. 4.3b-c of handouts).
• Coriolis force in action:
  • A nice applet on Coriolis and centrifugal forces.
  • The script of Peter Bowyer's simulation of Coriolis force on a projectile (before you can run it you need to install Python and VPython - instructions are available on the download pages for Python and VPython. (See also Peter's own website.)
  • Satellite image of a cyclone over the Atlantic from Tuesday, 6 Dec 94 (The night the liner Canberra lost electrical power in rough weather in the Channel). The wider picture: the same storm in relation to Europe and North Africa, from visible or Infra Red images.
  • Super Typhoon Winnie photographed from the Space Shuttle (from the Astronomy Picture of the Day archive).
  • The bathtub vortex: old chestnut about the water swirling in opposite senses as it leaves the bath depending on whether you are in the Northern or Southern hemisphere.
• Some fun with Foucault's pendulums.
• Here is Foucault's pendulum at the Franklin Institute.
• A note on invertible matrices and one on conjugated/transposed ones. This is even more useful.
• A reminder on Prosthaphaeresis Formulas (see Sect. 6.4.1 of lecture notes): from your school days !!!
• Animations of wave-like motions in one-dimensional crystals.
• Problem Solving Hints from M Barnhill at the University of Delaware