Physics/Astro C180: Order-of-Magnitude Physics

See bcourses.berkeley.edu for the up-to-date version.

Instructors

Eugene Chiang (echiang [at] astro.berkeley.edu)
GSI: TBD

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

Tuesdays and Thursdays, 3:30–5:00 p.m., Physics 251.
Bi-weekly “Thursday Labs” (in lieu of lecture), 11:00–12:30 p.m., 127 Dwinelle (Berkeley’s “Test Kitchen”).

Format

Weekly lectures.
Weekly problem sets, due Thursdays in class.
Bi-weekly Thursday labs (in lieu of lecture) where groups of 1–3 people solve problems in real time.
Course hand-out from first class (PDF).

Grading

Problem Sets: 50%
Thursday Labs: 25% (participation is sufficient for full credit)
Final Exam (3 hours; take-home): 25%
Letter grade assignment: A (≥ 90%) / B (75–90%) / C (65–75%) / P/NP or S/F: dividing line is at 65%.

Texts

There is only one 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 problems.

Sanjoy Mahajan is in the process of writing a textbook on order-of-magnitude physics. I cannot recommend this book more: it is lucid, funny, and captures the spirit and practice of this course.

Aside from Sanjoy’s textbook, a few order-of-magnitude textbooks I like include:

Consider a Spherical Cow: A Course in Environmental Problem Solving by Harte. A physicist by training, John Harte has taught environmental science and OOM estimation at Berkeley to high acclaim for many years.
Consider a Cylindrical Cow: More Adventures in Environmental Problem Solving by Harte. The exciting sequel.
Back-of-the-Envelope Physics by Swartz. Concise, readable, quantitative set of questions and answers, written by an Oersted Medalist.
Physics to a Degree by Raine. A wonderful set of problems and solutions.
The Flying Circus of Physics by Walker. Fun smorgasbord of questions with answers and pointers to the literature.

Some of the course material is drawn from these excellent texts:

Gases, Liquids, and Solids by Tabor (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
Random Walks in Biology by Berg
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

In the 1960s, the National Committee for Fluid Mechanics Films, led by Ascher Shapiro of MIT under the auspices of the National Science Foundation, created a set of beautiful and entertaining films on fluid dynamics. These have been uploaded to YouTube courtesy of Barry Belmont. The films come with a nearly complete set of notes.

Berkeley Physics Colloquia

Click here for webcasts of the Berkeley Physics Colloquia.

Problem Sets

Tuesday Labs (127 Dwinelle)

Handwritten solutions for Lab 2 — Lab answers (images):

Handwritten solutions for Lab 3 — Lab answers (images):

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.”

Everyday Estimation

Sample questions

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 the dispersion relation for water waves
Power scalings for monopoles, dipoles, and quadrupoles
Sample questions

Miscellaneous

Sample questions

Tips when estimating

The question matters.
Substitute / work by analogy.
Think in bulk.
“Steady-state” is your friend.
Do it another way to check.
Apply common sense.
“Use the Force.”
Convert money into salaries.
Numbers are meaningful only when normalized or compared.
Itemizing is OK, but look for shortcuts.
Take no prisoners.