A few comments on relativity

Transcription

1 Review

2 A few comments on relativity Relativity is a theory about the geometry of space and time Minkowski space (whiteboard) What happens in the barn paradox if the doors remain closed? Physics, not geometry. Someone will get hurt Questions about mass.

3 From Warmup Not gonna lie, the class was awesome. It made the numbers enjoyable and the physics enjoyable. This is ridiculous, but I would recommend another problem or two on most of the wave section Homework's, there is something to just spending a lot of time to really learn it all and have it stick. This is the hardest class I have ever taken in my life. It's also the class I think I've learned the most in. After all is said and done, it was a good experience. I just think the tests should be a little easier for future generations! This class as a *lot* of work, but it surprised me how much I came to enjoy the homework (at least in retrospect). I learned a lot from this class and appreciate all the work Dr. T put into helping me be somewhat successful in it this semester. A Tachyon orders a drink. The Tachyon walks into a bar. Also, In order to keep from cheating from a human frame of reference, Tachyons take tests with all the answers written and erase them one by one.

4 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 )

5 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)

6 Thermodynamics Calorimetry (conservation of energy) Heat Capacity/Specific Heat Latent heat (phase transitions) Evaporative cooling Heat flow Convection Conduction Radiation

7 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

8 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

9 Waves Wave equation/solutions Properties Amplitude Velocity Frequency Wavenumber Angular Frequency Waves carry energy

10 Complex Numbers Rectangular vs Polar representations Operations Addition, Subtraction, Multiplication, Division Complex Conjugate Absolute value Euler s Formula Used: Solve the wave equation Reflection/Transmission Optics (multiple slits)

11 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

12 Fourier Transforms Express function in terms of frequencies Calculating coefficients Relation to harmonics and musical tones Dispersion (velocity depends on frequency)

13 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

14 Wave Optics Wave phase Optical path length Interference Multiple Slits Diffraction Gratings (many slits) Waves in 3D Polarization (vector) Wave-vector (relation to velocity)

15 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

16 From Warmup Thanks for a great semester! I learned a lot! Thanks for the fun semester! 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.