Physics Stuff
Odds and Ends for the Classroom and Beyond
Some answers, useful resources and more questions.
A theory is more impressive the greater is the simplicity of its premise, the more different are the kinds of things it relates and the more extended its range of applicability…”
-Einstein
Unification and Concept Mapping
Throughout Physics we use a guiding Law that snapshots in time of systems all possess same energy content. Newton's Laws of motion unify phenomena that would otherwise appear distinct. Concept maps collate disparate ideas and provide a picture of how different viewpoints of a phenomena can resolve outstanding "how" questions (if not "why" questions).
Newton's Laws of Motion, Sound and Heat
Three ways of tackling problems – by Force, Field or Energy consideration. Force and energy related though application of force (to the system) over a displacement – either against a (conservative field such as) gravity or non-conservative slide against friction. Force and Momentum related by the application of an impulse (force over a period of time) to change momentum of system. Duality here (Force,Displacement)=<Energy> and (Force, Time)=<Momentum> whereas the dual variables arising from the symmetry of space are <Energy,Time> to give conservation of Energy and <Momentum, Space> to give rise to conservation of Momentum.
Deal with full bulk (turning moment, Angular momentum and Moments of Inertia) or idealize to center of gravity from which all forces seen to act from and on. If properties of bulk itself of interest as in Materials science, deal with Stress-Strain.
Everything is in the Phasor Diagram – know your Radians! Waves are just cycloids of clock-faces turning at phase speed while being translated at speed c. Know the field which creates oscillator’s periodicity – gravity for pendulum, spring constant-tension for spring, phonons for sounds, electromagnetic for vibrating water molecules,….
Force Vector to Force Field
Throughout the course we use Vectors or (Scalar and Vector) Field concepts to calculate the strength of interactions between systems of interacting bodies. Fields remove the Action at a distance problems of Newton’s Law of Gravitation (Non-contact force). Concept maps provide a picture of evolution of ideas and how a new concept (field) can resolve outstanding "how" questions such as “How does the force propogate through space instantaneously from one body to another?".
Two evolutionary routes from Newton: One goes from Newton to Einstein emphasizing change status of time and space while the other goes to Plank emphasizing non applicability of Newtonian physics to the Microscopic World. Maxwell's use of Faraday field unifies optics and electromagnetism.
Duality of Views: Wave or a Particle?
Throughout course we see a either wave or particle interpretations to explain phenomena. This is a historical reflection of the evolution of our theories. Light for example has come full circle from Newton’s corpuscular theory through to Huygens waves and back to Plank’s Wave packets.
Particle picture can explain all phenemena such as partial reflection from two surfaces of oil on water – beyond scope of course: QED.
Concept map collate how new particle picture is superior to wave for describing particle interactions in matter and so can resolve outstanding "how" questions (if not "why" questions).
With the significance of the wave Picture the Simple Harmonic Oscillator is emphasised. SHM and phasor diagrams are important!