ASTRONOMY 250:  ORDER-OF-MAGNITUDE PHYSICS



Goals
  • Develop order-of-magnitude problem solving skills (useful in life, research, and qualifying exams).

  • Learn how to solve everyday physics problems where your own experience can serve as a helpful guide.
Time and Place
  • Mondays and Wednesdays 2:00--3:30 pm, Hearst Mining 310
Format

Texts
  • There is only 1 required text for this class: the Astro 250 COURSE READER, available for purchase at Copy Central on Bancroft. We will refer to the reader throughout lecture, and its contents may be useful for the problem sets.

  • Sanjoy Mahajan, a former TA of Caltech's OOM class, is in the process of writing a textbook on order-of-magnitude physics. You can access his lucid work-in-progress here.

  • Some of the course material is drawn from these excellent texts:
    • Gases, Liquids, and Solids by Tabor (this is the first-year undergraduate text at Cambridge University)
    • Introduction to Solid State Physics by Kittel
    • Physical Fluid Dynamics by Tritton
    • Fundamentals of Fluid Mechanics by Munson, Young, and Okiishi
    • Fluid Mechanics by White
    • On Size and Life by McMahon and Bonner
    • Music, Physics, and Engineering by Olson
    • The Science of Musical Sound by Pierce
    • Waves and Oscillations by Crawford
    • and our trusty rag Physics Today which occasionally has nice tutorial pieces

    Movies

    Berkeley Physics Colloquia

Problem Sets

    PS 1: Due Wed Jan 28. Postscript version here. PDF version here
    PS 2: Due Wed Feb 4. Postscript version here. PDF version here
    PS 3: Due Wed Feb 11. Postscript version here. PDF version here


    PS 4: Due Wed Feb 25 (ONE WEEK SHIFT BECAUSE OF HOLIDAY). Postscript version here. PDF version here
        PS 5: Due Wed Mar 4. Postscript version here. PDF version here
        PS 6: Due Wed Mar 11. Postscript version here. PDF version here
       

    PS 8: Due Wed Apr 1. Postscript version here. PDF version here
        PS 9: Due Wed Apr 8. Postscript version here. PDF version here
    PS 10: Due Wed Apr 15. Postscript version here. PDF version here
        PS 11: Due Wed Apr 22. Postscript version here. PDF version here
        PS 12: Due Wed Apr 28. Postscript version here. PDF version here
        PS 13: Due Wed May 6. Postscript version here. PDF version here
   
   

Topics
  • The Virtues of Estimation
    • It's fun.
    • Develops physical intuition in a way that solving complicated equations might not.
    • Enables you to learn different subjects efficiently.
    • Enables you to decide whether a research problem is worth attacking.
    • Enables a check on numerical solutions.
    • Sometimes you actually know the answer, but only fear and self-doubt prevent you from realizing it. If the class trains you to stop and think before reflexively saying "I don't know", then we will consider it a success.
    • Even if it turns out you were wrong in your initial estimate, you will appreciate precisely why you were wrong (i.e., you can pinpoint exactly which factor you mis-estimated). As a result, you will be less likely to forget the answer, and you will better appreciate the subtlety of nature. "It is better to have estimated and erred than never to have estimated at all."
  • Material Properties
    • Atomic sizes and binding energies
    • Densities
    • Latent heats of vaporization and of fusion
    • Specific heats
    • Coefficient of thermal expansion
    • Elastic moduli
    • Yield stresses
    • Surface tension
    • Kinematic viscosities for gases and liquids
    • Thermal diffusivities/conductivities of insulators (Diffusion equation: solving equations without solving them)
    • Electrical conductivities of metals
    • Permanent magnets
    • SAMPLE QUESTIONS
  • Buckingham Pi Theorem
    • Buckingham Pi: If there are m physical variables defined in terms of n independent fundamental quantities, then there are m-n independent dimensionless groups.
    • Limitations of Buckingham Pi
      • Must pray that dimensionless coefficients are order unity
      • When m-n > 1: what combination?
      • When dimensionless quantities are desired: what exponent?
    • SAMPLE QUESTIONS
  • Fluid mechanics
    • Pressure Drag Laws
      • Subsonic: Free molecular, Stokes, Turbulent
      • Supersonic
    • Skin-Friction Drag Laws
      • Laminar boundary layer
      • Turbulent boundary layer
    • Flying
      • Parasitic drag (waste power) = Pressure + skin-friction
      • Induced drag (useful power) = Fighting gravity
      • Minimum power for flying vs. size, from hummingbirds to 747s
    • Wave-Making Drag and the Froude number
    • Ekman Boundary Layers
    • SAMPLE QUESTIONS
  • Waves and Sound
    • Applying the Buckingham Pi Theorem to derive dispersion relation for water waves
    • Power scalings for monopoles, dipoles, and quadrupoles
    • SAMPLE QUESTIONS