Kevin Zhou 2020/2021 Physics Olympiad Training
Syllabus
1 Course Structure
This course is structured around weekly problem sets. Each will have about 30 problems, ranging in
difficulty from F = ma to IPhO and beyond. Fundamentally, your learning will come from working
on this diverse set of problems.
At the end of the week, we’ll have an online meeting to discuss the problems and evaluate
your solutions. Throughout the week, you can contact me at any time by chat or email to ask
for clarifications or hints on the problem. Don’t hesitate to do this, because this is the essential
ingredient that makes tutoring better than learning from a book! You can also ask your fellow
students, or the TA, in the course group chat.
Usually the entirety of the class will be devoted to discussing problems; I won’t spend much
time introducing the basic material. You should already know calculus-based physics at the level
of Halliday and Resnick. Each problem set will also come with an assigned reading from some of
the textbooks listed below. I expect you to do any necessary reading on your own, doing extra
problems from the textbooks if necessary.
Your problem sets will be stored in a personal Dropbox folder. Official solutions to the problems
will be added to the folder before each class. The solutions were written by the course TAs, Sean
Chen and Gopal Goel. Both of them were USAPhO campers and IPhO gold medalists, and if you
have any questions about the problems, solutions, or life in general, feel free to contact them!
2 Problem Sets
The problems are chosen so that all of them demonstrate different ideas, so you’ll get more out
of the course the more you do. That said, it certainly isn’t necessary to do every problem. Every
problem will have a point value from 1 to 5, and each problem set comes with a cutoff which is
roughly 60% of the point total. If you reach this cutoff, you’ll have a good understanding of the
material. Participants aiming at IPhO gold medals should try essentially everything.
Problems marked with [A] are “advanced”. This doesn’t mean that they’re trickier, but rather
that they require more sophisticated mathematical techniques. These problems are less relevant to
Olympiad physics but are chosen to demonstrate interesting things; feel free to skip them.
If you’re interested in USAPhO prep you should attempt all of the USAPhO problems, while if
you’re interested in IPhO prep you should attempt the international-level (IPhO, APhO, WoPhO,
GPhO, EuPhO) problems. However, these latter problems are also valuable for USAPhO contestants.
Don’t be intimidated by them; they are usually worth 4 or 5 points, but that’s just because of their
length. The difficulty per time for older IPhOs is on par with current USAPhOs, and I don’t use
problems that are unreasonably hard. Often these longer problems have a lot to teach, since they
have the time to do a more complete analysis of a physical system.
Some problems will be marked with a clock. They should be done under realistic conditions,
which means you should use only pencil, paper and an officially allowed calculator. During this time
you should write a solution by hand, with the same level of detail you would for a real Olympiad. If
you run out of time but you’re still making progress, feel free to continue, but draw a line on your
solution indicating when time ran out. Common time limits will be
01W – 22.5 minutes, 01m – 45 minutes, 01h – 100 minutes
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Kevin Zhou 2020/2021 Physics Olympiad Training
for a USAPhO A, B, and full modern IPhO problem respectively. (Older IPhO questions are
much shorter, and may have correspondingly shorter times.) After finishing, immediately check your
answers and, if your solution was not complete, reflect on what you could have done differently.
3 Writing Solutions
You should submit your solutions within a day before class. For ease of reference, organize all your
solutions for one problem set in a single PDF, and all PDFs in your Dropbox folder.
As stated above, for timed problems your solutions must be in handwritten Olympiad solution
format, and scanned. For all other problems, handwritten solutions are also preferred, but you can
also use LaTeX, either locally or online at Overleaf. These solutions don’t have to be extremely
detailed: you don’t have to show all your algebra explicitly, and you don’t have to restate anything
written in the question. In general, I’m more concerned with the structure of the solution than the
algebraic steps. That is, emphasize the ideas you used to write down the equations, as much as
how you solved them.
4 Textbooks and Resources
We’ll be using a wide variety of textbooks and resources. The most important are marked with
stars. Be careful to get the right edition!
• ?? Halliday, Resnick, and Krane, Physics, 5th edition. This book contains the foundational ma-
terial required; you should know it forwards and backwards. Even today, a solid understanding
of it is enough to get a gold medal at the IPhO, though of course more knowledge always helps.
• Mahajan, Street Fighting Mathematics. A short, useful book about dimensional analysis and
estimation. Also see The Art of Insight, a longer work by the same author on the same themes.
• ? Kleppner and Kolenkow, An Introduction to Mechanics, 1st edition. Used at MIT, written
more like a physics book. Also has good problems, with a practical emphasis.
• ? Morin, Mechanics. Used at Harvard, written more like a math book. Has a large stock of
elegant, tricky, if sometimes contrived mechanics problems. Also contains an excellent, careful
introduction to special relativity.
• Schey, Div, Grad, Curl, and All That. A well-written, intuitive vector calculus book, with lots
of good pictures. Also see the excellent MIT OCW 18.02 lectures.
• ? Purcell and Morin, Electricity and Magnetism, 3rd edition. Does electromagnetism with
vector calculus and relativity baked in. Most famous for using relativity to derive magnetism,
rather than just postulating it. Has well-written problems that provide insight.
• French, Vibrations and Waves. A very nice and accessible exposition of mechanics waves once
used at MIT. Covers the wave equation, resonance, and normal modes; doesn’t spend much time
on specific waves. Also see Morin’s Waves book draft, which is somewhat more sophisticated.
• Crawford, Waves. An excellent book on all aspects of waves and oscillations, with hundreds of
real-world examples and home experiments; slightly more sophisticated than French.
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Kevin Zhou 2020/2021 Physics Olympiad Training
• Hecht, Optics, 5th edition. A well-written reference for interference, diffraction, and geometrical
optics, if a bit too technical for the Olympiad.
• Agarwal and Lang, Foundations of Analog and Digital Electronic Circuits. An accessible book
if you want to dig deeper into electrical engineering.
• Fermi, Thermodynamics. A first thermodynamics book that rigorously and methodically devel-
ops the subject; no problems.
• ? Blundell and Blundell, Concepts in Thermal Physics, 2nd edition. A second thermodynamics
book, covering important applications, using multivariable calculus and statistical mechanics.
Much of it will be very useful, though we’ll skip the most technical parts.
• Schroeder, Thermal Physics. Another good and clear introduction at roughly the same level as
Blundell, but with more focus on the core issues and less on applications.
• Krane, Modern Physics, 3rd edition. Modern physics just means everything that was done in
the past hundred years, so this is an extremely broad area. Krane covers it in about the right
level of detail for the Olympiad, refraining from using higher math.
• Some students have handwriting that’s hard to read; if that’s you, see this advice.
• If you prefer lectures to books, there’s an exceptional amount of good content on MIT OCW.
The classic references are the 8.01 (mechanics) and 8.02 (electromagnetism) lectures by Walter
Lewin, which are mathematically elementary, but which have many interesting physical examples.
Also see the 8.03 (waves) lectures, and the accompanying problem solving recitations. If you’ve
ever wanted to start learning quantum mechanics, try the 8.04 lectures by Barton Zwiebach
(more clear) and Allan Adams (more energetic).
• Khan and Anderson, Conquering the Physics GRE. This book is a light review of the under-
graduate physics curriculum. You may also find it useful to try problems from the Physics
GRE, which is like the F = ma exam, but with less time pressure and covering more content.
• ? The Feynman Lectures on Physics. A wonderful source of physical insight. Most problem
sets will have some chapters assigned for entertainment and enrichment.
Besides past Olympiads and textbooks, problems are also sourced from the following books.
• ? 200 Puzzling Physics Problems and 200 More Puzzling Physics Problems. Tricky questions
written in Eastern European style. The first book is highly recommended; the second book
is at times too mathematically clever to be too relevant to Olympiads, but still lots of fun.
(Also see 300 Creative Physics Problems with Solutions, a good book with somewhat more
straightforward questions.)
• ? Handouts by Jaan Kalda. These handouts and formula sheets provide excellent training
for Eastern European style Olympiads. Very different in style from the USAPhO (e.g. more
circuits, less relativity/modern physics), but highly recommended. Excellent solutions written
by AoPS members are available here.
• Krotov, Problems in Physics. A collection of Russian Olympiad problems in typical style. This
is a much shorter, refined version of Irodov’s classic Problems in General Physics.
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Kevin Zhou 2020/2021 Physics Olympiad Training
• Levi, The Mathematical Mechanic. A fun book which gives slick solutions for many mechanics
and calculus problems.
• Povey, Professor Povey’s Perplexing Problems. A collection of simple but tricky undergraduate
admissions interview questions with neat historical anecdotes.
• Thomas and Raine, Physics to a Degree. A collection of well-motivated questions used for
undergraduate physics training, with many real-world applications.
• Cahn and Nadgorny, A Guide to Physics Problems. A collection of graduate school qualification
exam problems. Some great classic problems are here, though most are too technical to be
useful for Olympiad preparation.
• Cavendish Problems in Classical Physics. Another collection of classic problems, used for second
year exams in Cambridge back when things were more hardcore. Also see Thinking Like a
Physicist by Thompson, for more qualitative questions used in final year exams at Bristol.
• Pathfinder for Olympiad & JEE. This book is commonly recommended, but I advise against
reading it if you’re preparing for the USAPhO. The style is extremely different, and some
definitions, conventions, and notation differ in potentially confusing ways.
• You can also consult resources used by other countries’ physics teams. From easiest to hardest:
– Upgrade Your Physics, used by the British physics team.
– Physics Olympiad – Basic to Advanced Exercises, used by the Japanese physics team.
– Wang and Ricardo, Competitive Physics, used by the Singapore physics team.
You can also meet other students to discuss problems on the Physics Olympiad Discord server.
5 Olympiad Problems
You can access most of the Olympiad problems we’ll do using the following links.
• Recent F = ma and USAPhO exams can be accessed here.
• As part of this training, you’ll also have access to older F = ma exams, quarterfinals, semifinals,
and their solutions.
• You can access past IPhO exams here and past APhO exams here.
• We’ll also draw problems from the EuPhO, GPhO, EFPhO/NBPhO, BAUPC, BPhO, JPhO,
AuPhO, CPhO, IZhO, INPhO, and HKPhO. (For a partial list of other Olympiads, see here.)
Always download a local copy and open with a PDF viewer, like Adobe Acrobat, since browser
PDF viewers can mess up the math. EFPhO/NBPhO problems will not be timed, but if you’d like
to compare yourself against the competitors, this competition allows about 8 minutes per point (in
contrast to the 10 minutes per point in international-level competitions).
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6 Curriculum
An outline of the full curriculum is shown below. You can go through it in any order, though
generally each problem set within a topic requires the previous ones. Towards the end of the
year, we’ll also have three review problem sets and eight practice USAPhO exams. Units that are
especially relevant to USAPhO preparation are underlined. In all cases, the prerequisites are a
strong grasp of calculus, and the relevant material in Halliday, Resnick, and Krane. Prior exposure
to vector/multivariable calculus is useful, especially for thermodynamics and electromagnetism, but
not necessary.
• 2 weeks of problem solving.
– P1: dimensional analysis, limiting cases, series expansions, differentials, iterative solutions.
– P2: probability, multiple integrals, error analysis, data analysis, estimation.
• 8 weeks of mechanics.
– M1: kinematics. Solving F = ma, projectile motion, optimal launching. (P1 helpful)
– M2: statics. Force and torque balance, extended bodies.
– M3: dynamics. Momentum, energy and center-of-mass energy, collisions.
– M4: oscillations. Damped/driven oscillators, normal modes, small oscillations, adiabaticity.
– M5: rotation. Angular kinematics, angular impulse, physical pendulums. (P2 helpful)
– M6: gravity. Kepler’s laws, rocket science, non-inertial frames, tides.
– M7: fluids. Buoyancy, Bernoulli’s principle, viscosity, surface tension.
– M8: more dynamics. 3D rotation, gyroscopes, and tricky friction/rotation problems.
• 3 weeks of thermodynamics.
– T1: ideal gases, statistical mechanics, kinetic theory, the atmosphere. (M7 required)
– T2: laws of thermodynamics, quantum statistical mechanics, radiation, conduction.
– T3: surface tension, phase transitions, thermodynamic systems.
• 8 weeks of electromagnetism.
– E1: electrostatics. Coulomb’s law, Gauss’s law, potentials, conductors.
– E2: electricity. Images, capacitors, conduction, DC circuits.
– E3: magnetostatics. More circuits, Biot–Savart law, Ampere’s law, dipoles and solenoids.
– E4: the Lorentz force. Charges in fields, mechanical circuits.
– E5: induction. Faraday’s law, inductors, generators, superconductors.
– E6: circuits. RLC circuits, normal modes, diodes. (M4 required)
– E7: electrodynamics. More circuits, displacement current, radiation, field energy-momentum.
– E8: synthesis. Dielectrics, magnets, fields in matter, technology.
• 3 weeks of relativity.
– R1: kinematics. Lorentz transformations, Doppler effect, acceleration, classic paradoxes.
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Kevin Zhou 2020/2021 Physics Olympiad Training
– R2: dynamics. Momentum and energy, four-vectors, forces, string theory. (E4 helpful)
– R3: fields. Electromagnetic field transformations, the equivalence principle. (E7 required)
• 4 weeks of waves.
– W1: wave equation, standing waves, music, the uncertainty principle. (M4 required)
– W2: interference, diffraction, crystallography, real world examples. (E7 required)
– W3: sound waves, water waves, electromagnetic waves, gravitational waves. (M7 required)
– W4: geometrical optics, lens systems, optics and thermodynamics. (T2, E8 helpful)
• 4 weeks of modern physics.
– X1: semiclassical quantum mechanics, bosons and fermions. (M4, T2, W1, required)
– X2: nuclear, particle, and atomic physics. (R2 required)
– X3: condensed matter, astrophysics, and cosmology. (W3 helpful)
– X4: advanced topics that didn’t fit elsewhere. (M7, T3, E8, W3 required)
The core material relevant to the USAPhO consists of two weeks of problem solving, seven weeks
of mechanics, seven weeks of electromagnetism, and eight weeks of special topics, for a total of 24.
For example, one path you could take thorough the curriculum is P1, P2, M1–4, E1–4, M5–7,
T1–3, E5–7, R1, R2, W1, W2, X1. (This splits up the long topics so you don’t work on any one
for too long at a time.) There are eight further advanced units which are more relevant for IPhO
preparation.
The USAPhO/IPhO point distribution is very roughly as follows:
USAPhO IPhO (theory)
Mechanics/Fluids 30% 25%
Electromagnetism 25% 20%
Relativity 10% 15%
Thermodynamics 15% 15%
Waves 10% 10%
Modern 10% 15%
