Back of the Envelope, Ph 101 Order of Magnitude Physics

2025 Spring Term, Caltech

Lectures: Mon, Wed 1:00-2:30pm, 201 Bridge

Homeworks: Due 11:59pm on Thursdays (starting April 10) as pdf uploads to Canvas, the week after they are posted.

Final Exam: Due 2pm PDT Thursday June 5, 2025 for Seniors and Grad students. Due 2pm PDT Thursday June 12, 2025 for Frosh-Juniors.

Prof:   Sterl Phinney  [final]
        316 Cahill
        esp [AT] tapir.caltech.edu
	Office hours: TBD

TAs:	Annika Dugad [PS 1, 4, 5, 8, final]
	[recitations 1, 5]
        adugad [AT] caltech.edu
	Office hours: W 5-6pm, B157 West Bridge

	Yu Li [PS 2, 3, 6, 7, final]
	[recitations 3, 7]
	yuli2 [AT] caltech.edu
	Office hours: W 5-6pm, B157 West Bridge

	Kai L. Svenson [parts of PS 1, 3, 5, 7]
	[recitations 2, 4, 6, 8]
	ksvenson [AT] caltech.edu
	Office hours: Weds 5-6pm, B157 West Bridge



COURSE WEBSITE:

WWW: http://www.its.caltech.edu/~oom/

SYLLABUS:

The big picture: at the end of this course, you should be unafraid to estimate numbers you don't know, scale solutions, 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 should also have had fun and 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. And the demos are memorable.

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

Week
1       Estimation, Dimensional analysis, scaling
2       More scaling, Bulk Properties of materials
3       Properties of materials
4       Water waves, Sound waves and acoustics, musical instruments
5       Weather, oceans and atmospheres, climate change.
6       Birds, airplanes, helicopters, spacecraft, lift, drag, boundary layers
7       Non-renewable and renewable energy: physics and transitions.
8-9     student vote from topics below

Topics:

-Biomechanics and exercise
-OoM Economics, industry and finance.
-Order of Magnitude math.
-Earthquakes and their effects.
-atomic and nuclear physics; energy levels cross-sections and reaction rates.
-Meteors, meteorites, asteroids.
-Covid-19 and other virus spreading
-Astrophysical objects: stars, planets, cosmology, the anthropic principle.
-Biology: neurons, information processing. Evolution, metabolism, lifetime.
-Bombs, guns, torpedos, nuclear reactors, supernovae and other things
 that go bang.
-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)

HOMEWORK, GRADING and COLLABORATION POLICY

FINAL EXAM

The "final" will contain approximately six problems posed by the instructors, and count for 30% of your grade. 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.

CLASS PARTICIPATION

This, together with online mini-quizzes, will count for 10% of your grade. The class will be divided into groups of 3 or 4 students, and you will be asked to submit a name for your group. The groups will be called upon in lecture to make estimates. A well-justified roughly correct answer will get full credit. A reasonably-justifed but wildly incorrect answer will get half credit. Absence or lack of justification will get no credit.

HOMEWORK

Homework will count for 60% of your grade. 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 Canvas and/or 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 Canvas.

EXTENSIONS and LATE HOMEWORK POLICY:

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 on your problem set that you are using the extension.

If your extension homework is more than one week late, or if more than one homework is late by x hours, 0.1*ceil(x/24)*(maximum possible score) will be subtracted from your score (i.e. you lose 10% of the maximum possible score per day or fraction thereof). 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 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 Thursday will instead become due on Friday of that week.

GRADING

Your grade will be a mostly monotonic function of
g = [0.6(sum of homework scores)/(total possible) + 0.1(sum of class participation scores)/(total possible) + 0.3(score on final exam)/(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
20230.90 0.84 0.71 0.60
20210.90 0.83 0.70 0.60
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 and INTERNET RESOURCES POLICY:

Collaboration policy on the final exam:
  1. The "traditional" part of the exam will be closed book and closed computer-like devices. You may use a printed copy of 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. In particular, get it approved by Sterl at least a couple of weeks before the exam. But you should do all the final choice of problem, solving and writing yourself.

Collaboration and use of internet tools 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"). If you do use Google or other internet search methods to look up or check numbers, you must report that you did so, and give the sources you used on your homework. However, it is strongly recommended that you do your best to avoid checking numbers in this way.

Use of generative AI/Large Language models (ChatGPT and its many relatives: `AI')) or online tutoring sources (OT) as an aid to solving the homework problems, and searching for homework problems, or their close relatives online is strictly forbidden, and will be considered a violation of the Caltech Honor Code. See the PMA policy on AI, IR, OT.

Visual exchanges of information are also 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, published papers, and internet sources 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.