Back of the Envelope, Ph 101 Order of Magnitude Physics

2021 Spring Term, Caltech

Lectures: Mon, Wed 1:00-2:30pm Pacific Time, via Zoom (linked in the course Canvas module)

Final Exam: Due 2pm PDT Thursday June 3, 2021 for Seniors and Grad students.

Due 2pm PDT Wednesday June 9, 2021 for Frosh-Juniors.

Prof:   Sterl Phinney  [final]
        316 Cahill
        esp [AT]
	Office hours: TBD

TAs:	Alexander Zlokapa  [PS 1, 5, final]
        azlokapa [AT]
	Office hours: TBD

	Stella Wang [PS 2, 6, final]
	stellaw [AT]
	Office hours: TBD

	Nikita Klimovich  [PS 3, 4, 7, 8, final]
        klimovich [AT]
	Office hours: TBD

        When not sleeping, will
        assist with lectures and demos,
        and provide fur samples




The big picture: at the end of this course, you should be unafraid to estimate numbers you don't know, make approximations in equations, and figure out what physics is important in a given experiment or situation, and see whether an explanation or number is worth pursuing further. You will should also have understood a lot more physics. It is unlikely that you will learn much of this if you do not attend the lectures: estimation and approximation are at least as much art forms as a science.

Approximate class outline (may change depending on student and instructor enthusiasms...)

1       Estimation, Dimensional analysis, scaling
2       More scaling, Bulk Properties of materials
3       Properties of materials, transport
4       Aerosols, SARS-Cov-2 and Covid 19
5       Non-renewable and renewable energy: physics and transitions.
6       Weather, oceans and atmospheres, climate change.
7       Birds, airplanes, helicopters, spacecraft, lift, drag, boundary layers
8-9     student vote from topics below

-Sound waves and acoustics, the ear, musical instruments, recording
-Biomechanics and exercise, water waves
-Economics, industry and finance.
-Bombs, guns, torpedos, nuclear reactors, supernovae and other things
 that go bang.
-Order of Magnitude math.
-Earthquakes and their effects.
-Nuclear and atomic physics; cross-sections and reaction rates.
-Astrophysical objects: stars, planets, cosmology
-Biology: neurons, information processing. Evolution, metabolism, lifetime.
-Challenge me!

TEXTBOOK: None required, but highly recommended (depending on your interests and background) supplemental readings are:

Feynman Lectures on Physics, Vols 1-3
by Richard Feynman
ISBN 978-0465023820
(Basic Books)
Or read 'em free online
Physical Fluid Dynamics
by D. Tritton
ISBN 978-0198544937 (2nd Ed)
(Oxford University Press)
Gases, Liquids and Solids
by D. Tabor
ISBN 978-0521406673
(Cambridge University Press)
Street-Fighting Mathematics
by Sanjoy Mahajan (a former Ph 101 TA)
ISBN 978-0262514293 (3rd Ed)
(That Other IT Press)
The Art of Insight in Science and Engineering
by Sanjoy Mahajan (a former Ph 101 TA; book is based on an early version of Ph 101)
ISBN 978-0262526548
(That Other IT Press)



The "final" will contain approximately six problems posed by the instructors. You may optionally replace one of these problems with an original one you pose and solve by yourself. You may work on this problem before the exam. It may not be one you find solved anywhere, the solution must be entirely of your own making. If you wish to exercise this option, it is recommended that you ask Sterl midway through the term, and at least a week before the final, if your problem is an acceptable one. Your grade will be determined by both how interesting and original the problem is to Sterl and the TAs, how rich it is in physics, and how you elegantly you solved it by order of magnitude methods.

Final exams: see due dates above.


There will be approximately weekly homework sets due as pdf files uploaded within Canvas before the beginning of Wednesday's class, one week after they are posted on this website (see homework link at left). It is your responsibility to access the problem sets and to turn them in on time. Please remember to reduce the resolution so the file size is reasonable (< 500 kbyte/page, < 8Mbyte total). 100Mbyte image files are unnecessary and unpleasant for everyone involved in uploading and downloading.

Solution sets will be posted on the website.


You may take one full-credit one-week extension on a problem set during the term. No need to contact the instructors or the TAs, just write it on your problem set. If that homework is more than one week late, or if more than one homework is late, it will not be accepted nor graded unless prior arrangements with Sterl have been made as described below. Other extensions will only be granted for extraordinary reasons ---documented health issues, family emergency, etc. You must consult Sterl in person or by e-mail, before the homework is due. Some sort of proof of extenuating circumstances (e.g., certificate from the health center, counseling center, or Dean of Undergraduate Students) will be necessary. The one free extension in the previous bullet item is designed to satisfy other reasons such as ``I had too much other work'', or ``I was preparing for a conference'', so don't waste it and expect additional extensions for such reasons. In the event that Senior Ditch Day falls on a Monday, Tuesday or Wednesday, the homework that would have been due that Wednesday will instead become due on Friday of that week.


Your grade will be a mostly monotonic function of
g = [0.7(sum of homework scores)/(total possible) + 0.3(score on final)/(total possible)].
Because new topics and new problems are given every year, and the mix of students varies, Sterl determines the connection between letter grade and numerical score by looking at natural breaks in the final distribution: there are no fixed cutoffs and no predetermined curve. However as a very rough guide, here are the grade cutoffs for previous years:

YearA+ A B C
20190.90 0.80 0.70 0.55
20170.93 0.89 0.75 0.65
20150.82 0.75 0.60 0.45
20090.90 0.80 0.67 0.50
20070.90 0.85 0.75 0.60


Collaboration policy on the "final":
  1. The "traditional" part of the exam will be closed book and closed computer-like devices, except for Purcell's sheet of useful numbers.
  2. if you choose the option to write one of your own problems to replace an exam problem, you may talk about general topics, reference papers and equations with anyone as you are choosing the problem and trying out ideas. But you should do all the final choice of problem, solving and writing yourself.

Collaboration on the homework is limited. You must first try every homework problem BY YOURSELF for at least 30 minutes without external help (human or internet), other than looking up fundamental equations (e.g. Navier-Stokes, Schroedinger, Planck black-body, etc) in the recommended texts. This is the fun, OoM part. For estimation problems, this in particular means you must work out an answer using only what is in your brain before typing anything into a search engine. If subsequent Googling suggests your estimate was way off, you can then try to understand what went wrong with your estimate (or, not infrequently, with the dubious web "information").

Visual exchanges of information are strictly forbidden -you may not trade equations, graphs, or look at other people's solution sets from this or any prior year, or from child or grand-child Ph 101-like courses at other universities.

You may consult books and published papers to learn or remind yourself of relevant physics. The recommended texts are (surprise) recommended.

If after spending 30 minutes on a problem you are still stuck on it, you may TALK about the homework with the TA or your fellow students, but all exchanges of information must be general in nature and either exchanged verbally, or with modern replacements for talking (i.e. texting and emailing is ok too, as long as details are avoided -see below). For example the following QandA is ok Q: "I got a density of one atom per cubic km. Isn't that awfully low for lead at room temperature and pressure? A: "Yup, sure is. What variables did you include in your Buckingham Pi list? Oh, I think quantum mechanics is relevant here. Why did you leave out hbar? The following one is NOT OK: Q: "I'm stuck on problem 2. Can you help me?" A: "Sure. You take equation 3.12 of this book, insert equations 2.5 and 3.2, integrate and you should get the right answer which is V k squared over pi squared".

After any discussion with others, you must write up your own homework by yourself, without reference to anyone else's.

In real research, no one else knows the answer to the problems you work on (otherwise why would you be doing them?), so the most important thing you can learn from homework is how to think and solve for yourself, and be confident in your answers.