Review
Where we ended last time: A nuclear power plant generates 10 million Watts of power nonstop for a day. How much less do the fuel rods weigh at the end of the day? (Careful with units!) A. around 0.0001 grams B. around 0.01 grams C. around 1 gram D. around 0.1 kg E. around 10 kg
A few comments on relativity Relativity is a theory about the geometry of space and time Minkowski space (space + time = spacetime) What happens in the barn paradox if the doors remain closed? Physics, not geometry. Someone will get hurt http://what-if.xkcd.com/1/
From Warmup Do you know anything about the cosmic censorship conjecture? It is a conjecture about the nature of singularities in General Relativity Please... don't say we look like this when we take the test... I don t know for sure, but it s basically how I ve always pictured you
Preparing for the final Make a list of concepts Use these slides as a STARTING point How do concepts relate to one another? Review the equation sheet from last semester How do the equations relate to the concepts? Work through examples in the text Try it without looking at the answer first Peek at the answer second Carefully read the book s solution third Review old midterms (especially problems you missed) Review Homework (particularly the Extra-Problems )
Fluids Pascal s Law (changes in pressure transmitted through fluid) Archimedes Principle (buoyant force = weight of displaced fluid) Continuity equation (conservation of fluid) Bernoulli s equation (conservation of energy)
Thermodynamics Calorimetry (conservation of energy) Heat Capacity/Specific Heat Latent heat (phase transitions) Evaporative cooling Heat flow Convection Conduction Radiation
Thermodynamics First law of thermodynamics Heat Engines/Refrigerators/P-V Diagrams Efficiency Coefficient of performance (COP) Types of processes Isothermal Isobaric Isovolumetric Adiabatic Second law of thermodynamics Carnot engine/efficiency
Thermodynamics Macroscopic vs. Microscopic descriptions of a system Kinetic theory (temperature = average kinetic energy) Entropy Microstates / Macrostates Combinatorics (counting microstates) Temperature = (inverse) rate of change in entropy
Waves Wave equation/solutions Properties Amplitude Velocity Frequency Wavenumber Angular Frequency Waves carry energy
Complex Numbers Rectangular vs Polar representations Operations Addition, Subtraction, Multiplication, Division Complex Conjugate Absolute value Euler s Formula Used: Adding waves (super-position) Reflection/Transmission Optics (multiple slits)
Sound Sound Pressure wave/displacement Wave Intensity, Sound levels, Amplitude Harmonics, Beats, Standing Waves Boundary conditions Doppler Effect Moving source vs. moving observer Musical Scales
Fourier Transforms Express function in terms of frequencies Relation to harmonics and musical tones Dispersion (velocity depends on frequency)
Geometric Optics Huygens Principle Law of Reflection Snell s Law Index of refraction Lenses, Mirrors Objects vs. Images Virtual vs. Real Upright vs. Inverted Magnification Abberations Magnifier/Telescope Angular magnification
Wave Optics Wave phase Optical path length Interference Multiple Slits Diffraction Gratings (many slits) Waves in 3D Polarization (vector) Wave-vector (relation to velocity)
Relativity Time Dilation Length Contraction Space-time diagrams Events World lines Lorentz Transformations Energy and Momentum Relativistic momentum Energy/mass Relativistic mass vs. Rest mass
Topics and Relation to other courses Fluid Mechanics Physics 123 (Majors) Special Relativity Thermodynamics 360 121 Math 352 Math 334 230 Wave Mechanics We have covered a lot! You ve worked very hard. Optics 220 461 318 451-452 441-442 471 222
From Warmup Could we get feedback on the question(s) we submit? Sure If you want feedback, I ll send you an email individually. Generally you all came up with some really good questions. Some of the test questions are inspired by things you suggested, though I ve tweaked them a bit and/or changed the context. Some of your problems were very creative and show that you ve come a long ways in this class. You ve discovered that the principles we ve learned can be used to solve problems in a lot of different scenarios, and not just the canned textbook type of problems (e.g., a mass on an inclined plane). That was my personal goal for this class.
Thinking like a physicist You have been exposed to the topics of this course your entire life (fluids, heat, waves, light, maybe not relativity.) What could you possibly have left to learn? Physics is not so much a list of topics as a way of approaching problems Physics Education Research (PER) Most people think of the world in terms of Aristotelian physics Experience/Experiments -> Principles Principles allow us to extrapolate knowledge to new circumstances
Thinking like a physicist Contrast Physics 121 (Newtonian Physics algorithmic) Move beyond algorithmic problem solving into creative problem solving Ask: How do the principles determine the solution? Not: What are the mathematical steps to solve the problem? (These are secondary to our main purpose.) Analogy: We are building a scaffolding that you will fill in with Homework/Labs/other physics classes Take home exams ~2 problems that apply principles to new situations How to prepare: Extra problems on the HW sections This is hard/frustrating you ll have to trust me that it works I teach them correct principles and they govern themselves -Joseph Smith
From Warmup Thanks for all of your hard work! I've really enjoyed your class. Thanks! I ve enjoyed having you all in it! Conclusion We ve covered a lot of material Fluids, Heat, Waves, Optics, Relativity We ve learned a lot of new math Complex Numbers, Fourier Transforms, Waves in 3D You ve done a lot of work. You ve all come a long way and should feel proud.