Recommended list of problems

In what follows is a list of problems, selected on the basis of my personal preferences and sorted by topics. If you don't find your favourite problems here, please nominate!

Mechanics (incl. celestial mechanics)

From IPhO-s:
IPhO-1982-Pr2 - excellent problem on physical pendulum.
IPhO-1984-Pr2 - open-ended problem on oscillations dealing with an interesting natural phenomenon (seiches).
IPhO-1985-Pr3 - a problem on Kepler's laws with a real practical significance.
IPhO-1988-Pr2 - the physics of Maxwell's disc (note that the figure illustrating question 4 is disorienting and the respective official solution is wrong; assuming a long rope, a correct solution is reasonably simple).
IPhO-1989-Pr2 - a short problem on planetary dynamics requiring mathematical insight.
IPhO-1990-Pr3 - an excellent short problem on rotational dynamics requiring insight, but NB! official solution oversimplifies ellipticity calculations and you need to do the same: calculating the gravity field of an elliptical body is too mathematical (ignoring this effect gives correct of magnitude, though).
IPhO-1991-Pr1 - this will teach you the basics of the collision of bodies.
IPhO-1992-Pr2 - coupled oscillators in a physically meaningful context.
IPhO-1997-Pr1-Q5 - a problem on scaling laws; note: this problem was also on the Physics Olympiad of Soviet Union-1978.
IPhO-1998-Pr1 - a neat analysis of a rolling pencil.
IPhO-2000-Pr1-Q1 - straightforward physically, but teaching useful technical skills (tailoring solutions).
IPhO-2012-Pr1-Part-A - will test your physical and mathematical insight (about ballistic motion).
IPhO-2014-Pr1-Part-A - problem on a non-standard conservation law of a momentum-like quantity.
IPhO-2019-Pr1 - How a slinky falls - very nice physics!
From APhO-s:
APhO-2005-Pr1-Part-B - shows how to make use of the separation of fast and slow processes, and models reasonably a real-life situation (swinging).
APhO-2010-Pr1-Part-A - you'll learn about inelastic scattering on composite particles (the linked text is heavily modified to make it clearer).
APhO-2010-Pr1-Part-B - shows how to make use of a superposition of linear waves.
APhO-2011-Pr2 - a nice model of a real-life problem (creaking door).
APhO-2011-Pr3 - a (relatively) simple model of phase transition (for a birday balloon); tests your physical insight.
APhO-2016-Pr1 - conceptually not a really difficult problem, but you can polish your technical skills (using vector algebra you can find shorter-than-official solutions).
APhO-2017-Pr2 - a nice problem on celestial dynamics - conceptually not too challenging.
Physics Cup:
Physics Cup 2012 - Pr1 - a tricky problem on Kepler's laws.
Physics Cup 2012 - Pr4 - will test your physical and mathematical insight, including vector analysis (dynamics).
Physics Cup 2019 - Pr3 - a simple-for-Physics-Cup problem on parabolic trajectories.
From Estonian-Finnish Olympiads:
Est-Fin-2003-Pr5 - separation of fast and slow processes (vibrating surface).
Est-Fin-2005-Pr3 - tests your understanding of Kepler's laws in several ways.
Est-Fin-2005-Pr4 - something for polishing your skills in hydrodynamics (centrifugal pump).
Est-Fin-2006-Pr5 - tests your insight when dealing with pressure forces (air-filled bag).
Est-Fin-2006-Pr6 - geometrical approach to static equilibrium problems.
Est-Fin-2007-Pr2 - linear stability analysis for a slightly tricky geometry (stressed elastic rod).
Est-Fin-2009-Pr7 - develops model building and qualitative estimation skills (breaking soap film).
Est-Fin-2011-Pr6 - very similar to the APhO-2011 Pr2 (violin vs creaking door).
Est-Fin-2012-Pr1 - a many-part problem testing your understanding of planetary dynamics, skills in kinematics, and separation of long and short time-scales.
Est-Fin-2014-Pr6 - tests your physical insight (kinematics).
Est-Fin-2015-Pr4 - a problem on optimal Keplerian trajectories.
Est-Fin-2016-Pr1 - about fuel consumption and interpreting graphs
NBPhO-2017-Pr2 - yet another problem on Kepler laws.
NBPhO-2018-Pr1 - planetary motion NOT on Kepler laws - a surprising 3-body system.
NBPhO-2019-Pr1 - an optimization task with Kepler laws.
From GPhO-s:
GPhO-2016-Pr1BC - you can get some insight into tightrope walking + learn about Kapitza's pendulum.
GPhO-2017-Pr2 - a fairly tricky problem with a water-filled tube.
GPhO-2019-Pr1C - only in case you still hadn't had enough problems on Kepler's laws;
GPhO-2019-Pr3B - about Rayleigh-Taylor instability which has an important role to play in physics.
From EuPhO-s:
EuPhO-2017-Pr1,7 - Pr1 is about natural modes of a hanging rope; Pr 5 is a nice dynamics problem with collisions.
EuPhO-2018-Pr1 - very classically-looking but not-so-easy problem.
EuPhO-2019-Pr3 - about the shape of water stream coming out from a water hose.


From IPhO-s:
IPhO-1985-Pr2 - quite straightforward problem, but you'll learn what is the Hall effect.
IPhO-1987-Pr3 - this simple model of waveguides tests your skills of dealing with AC and building electro-mechanical equivalence.
IPhO-1993-Pr1 - a problem testing your insight in electrostatics and making use of the characteristic time scales (RC).
IPhO-1994-Pr2 - a nice problem dealing with currents in superconducting circuits.
IPhO-1996-Pr1-Q5 - teaches useful tricks with superposition principle (Ampere's law).
IPhO-1996-Pr2 - teaches how to deal with unusual conservation laws (generalized angular momentum).
IPhO-2000-Pr2 - an excellent problem on the motion of charged particles in E and B fields.
IPhO-2002-Pr2 - teaches dealing with current densities, vector analysis and superposition principle; you can also try to prove the validity of the suggested equivalent circuit (using the method electrical imaging, i.e. constructing the current distribution as a superposition of known valid solutions of the Maxwell equations).
IPhO-2004-Pr1 - tests your understanding of electrostatics (ping-ponging disc inside a capacitor).
IPhO-2011-Pr3 - scattering of an ion by an atom (tests your capability of selecting physically appropriate solutions and interpretation of the lack of solutions).
IPhO-2012-Pr1-Part-C - dealing with magnetic fields in the presence of superconductors (Q3 is really tricky).
IPhO-2012-Pr2 - tests your understanding of electrostatics (Kelvin water dropper).
IPhO-2014-Pr1-Part-C Somewhat artificial and mathematical, but still a useful exercise on a LC-circuit with two degrees of freedom.
IPhO-2016-Pr2 A very nice problem on nonlinear voltage oscillations.
From APhO-s:
APhO-2001-Pr2 - a problem on the generalized momentum of charged particles with an emphasis on vector analysis (part 2 can be solved geometrically, simpler than in the official solution).
APhO-2009-Pr2 - a problem on magnetic dynamo and linear instability.
APhO-2011-Pr1 - a nice problem testing your insight in electrodynamics (Shockley-James Paradox).
APhO-2013-Pr1 - electrical imaging in cylindrical geometry (approach to the calculation of the RC-time is unnecessarily long).
APhO-2017-Pr1 - a very nice problem; once you study it, you'll understand why it is here under electromagentism.
APhO-2018-Pr1 - a problem with many subquestions, but you'll learn about coaxial wave guides, and a litte even about quantum computing.
Physics Cup:
Physics Cup 2012 - Pr2 - teaches how to calculate the magnetic fields in the presence of ferromagnetic materials.
Physics Cup 2012 - Pr5 - calculation of natural frequencies while making use of the separation of time scales.
Physics Cup 2012 - Pr6 - a nice problem covering electrical imaging, electrostatic pressure, and electrostatic energy.
Physics Cup WoPhO-2013 - Pr5(10) - dealing with magnetic fields in the presence of superconductors.
Physics Cup 2017 - Pr1 - a really tough problem on electrostatics...
Physics Cup 2017 - Pr2 - ... and on electric circuits.
Physics Cup 2018 - Pr1 - Infinite resistor lattices revisited.
Physics Cup 2018 - Pr3 - A single loop around a ferromagnetic coil - a really challenging task on magnetostatics.
Physics Cup 2019 - Pr1 - How polarizability is related to the added mass - one of the favorites of the contestants.
Physics Cup 2019 - Pr4 - Yet another infinite grid of resistors (why are there so many PhysCup problems on electrodynamics?!).
Physics Cup 2020 - Pr0 - A very nice problem on sheet resistance.
From Estonian-Finnish Olympiads:
Est-Fin-2006-Pr7 - tests your basic knowledge of cyclotron motion and ability of making appropriate approximations.
Est-Fin-2007-Pr3 - teaches about time focusing (phenomenon similar to wave breaking); a problem rooting from the IPhO-2001-Pr1-Q1.
Est-Fin-2010-Pr1 - somewhat artificial, but still a useful exercise (on using optimal reference frames).
Est-Fin-2012-Pr7 - a non-trivial problem on Ampere's force.
Est-Fin-2014-Pr1 - tests your understanding of circuits containing L and C in various ways.
Est-Fin-2015-Pr9 - a useful exercise on coupled solenoids and mutual inductance.
Est-Fin-2016-Pr4 - have you ever wondered how dimmer works?
NBPhO-2017-Pr7 - quite a tricky problem with zener diode in AC circuit.
NBPhO-2018-Pr5,7 - Pr 5: colliding magnetic balls in B-field - last task is fairly tricky; Pr 7 - a challenging AC circuit problem
From GPhO-s:
GPhO-2016-Pr2 - a simple approach to gravitational waves and LIGO experiments.
GPhO-2016-Pr3 - teaches about strong magnetic fields (incl magnetars).
GPhO-2017-Pr3 - a fairly challenging problem about acceleration of charged particles with shock waves.
GPhO-2019-Pr2Biii,iv - a little bit about TOKAMAK project.
From EuPhO-s:
EuPhO-2017-Pr3 - have you seen how a piece of superconductor can slide along magnetic rails? Here you can learn how it works.
EuPhO-2018-Pr2 - boiling water using a solenoid
EuPhO-2019-Pr2 - a rolling charged ball in magnetic field.


From IPhO-s:
IPhO-1987-Pr1 - not too tricky problem teaching nice physics (raining).
IPhO-1992-Pr2 - a solid problem on heat radiation with real-life implications (satellite in sunlight).
IPhO-1996-Pr1-Part-d - a small but useful exercise (triple-wall-thermos).
IPhO-1998-Pr2 - a problem dealing with the basics of mechanics and thermodynamics (ice flow and melting).
IPhO-2008-Pr3 - with a mathematical emphasis and with a prescribed approach, but teaching important atmospheric physics (adiabatic atmosphere).
IPhO-2010-Pr2 - a nice problem on chimney physics.
IPhO-2012-Pr1-Part-B - tests your insight into the physics of gas flows (turned out to be surprisingly difficult, with only one full solution among the contestants).
IPhO-2012-Pr3-Q4&6 - tests your understanding of the I law of thermodynamics and adiabatic processes (those familiar with standard protostar evolution models need to read the text carefully: the model is slightly modified).
IPhO-2014-Pr1-Part-B Somewhat artificial and non-realistic setup, but still a valid exercise on a polytropic process.
From APhO-s:
APhO-2007-Pr3-Task-A - quite mathematical, but teaches you that the conduction electrons do not form an ideal gas.
APhO-2010-Pr3-PartB - somewhat mathematical, but with a nice physics (sonoluminescence).
APhO-2014-Pr1 - an excellent problem on atmospheric circulation.
APhO-2018-Pr3 - a problem with too many simple subquestions (be warned!), but dealing with an interesting phenomenon - thermoelectric effect.
Physics Cup:
Physics Cup 2012 - Pr3 - teaches the basics of kinematic theory of gases.
Physics Cup WoPhO-2013 - Pr4(9) - a challenging problem on the laws of thermodynamics.
Physics Cup 2017 - Pr3 - with this problem, you can get some insight into adiabatic processes.
Physics Cup 2018 - Pr5 - black sphere: mean free path in vacuum - a really difficult problem.
Physics Cup 2019 - Pr2 - a simple-for-Physics-Cup problem on the 2nd law of thermodynamics.
From Estonian-Finnish Olympiads:
Est-Fin-2004-Pr7 - on Bernoulli law and heat balance (passive air cooling; similar to IPhO-2010-Pr2).
Est-Fin-2005-Pr7 - physics of the ventilation system of your zero-energy house.
Est-Fin-2006-Pr1 - on the humidity and mixing of cold and hot air.
Est-Fin-2008-Pr7 - a simplified version of the Pr3 from IPhO-2008 (rising smoke).
Est-Fin-2010-Pr2 - somewhat similar to IPhO-1996-Pr1-Part-d, but with a trickier geometry (thermos bottle).
Est-Fin-2011-Pr8 - a tricky problem on heat conduction.
Est-Fin-2013-Pr7 - an ordinary problem on heat radiation, but with a useful conclusion (a limit to the F-number of a lens).
NBPhO-2018-Pr8 - a small exercise with pressure work and energy balance.
NBPhO-2019-Pr6 - thermodynamics of a self-gravitating gas cloud.
From GPhO-s:
GPhO-2019-Pr2D - about inertial confinement fusion project.
From EuPhO-s:
EuPhO-2017-Pr2 - to polish your skills in kinetic theory of gases.
EuPhO-2018-Pr3 - a really challenging problem on surface energy.
EuPhO-2019-Pr1 - about the formation of ice pellets.

Wave optics and quantum mechanics

From IPhO-s:
IPhO-1990-Pr1-PartD - the basics of Bragg reflection (you can skip parts a, b, and c as these are not needed for solving d).
IPhO-1993-Pr3 - teaches several important concepts and techniques (electrostatic biprism).
IPhO-2003-Pr3-PartB - there are other similar problems, as well (e.g. IPhO-1993-Pr2), but this should be enough to get the idea (of radiation pressure).
IPhO-2005-Pr3 - while the whole problem is worth solving, the highlight is the last task (one can guess the right answer quite easily, but doing it properly requires a thorough understanding of the basic quantum mechanics - stationary states and line widths).
IPhO-2006-Pr1 - a Mach–Zehnder interferometer for neutrons.
From APhO-s:
APhO-2010-Pr3-PartB - somewhat similar application of the uncertainty principle was at IPhO-1988 (Pr 3), but this problem is neater.
APhO-2016-Pr3 - magnetic fields + quantum physics - about superconductors (there is an easier solution to Part D2 than the official ones).
Physics Cup:
Physics Cup 2012 - Pr3 - this turned out to be the most difficult problem of Physics Cup 2012 (laser speckles pattern).
Physics Cup WoPhO-2013 - Pr3(8) - a beautiful problem in various ways (bubbles in laser light).
Physics Cup 2019 - Pr5 - Echelle grating - a really difficult problem!
From Estonian-Finnish Olympiads:
Est-Fin-2003-Pr7 - a challenging problem on diffraction (stars through telescope in daylight).
Est-Fin-2004-Pr4 - tests your understanding of the interference on thin films.
Est-Fin-2005-Pr5 - on 2-dimensional interference patterns.
Est-Fin-2015-Pr2 - physics of short light pulses.
NBPhO-2018-Pr6 - another photon pressure problem.

Relativity, geometrical optics, etc

From IPhO-s:
IPhO-1984-Pr1 - a relatively simple problem on geometrical optics (mirage effect).
IPhO-1994-Pr1 - a nice problem on ultrarelativistic particles.
IPhO-1995-Pr1-PartC - a small exercise on relativistic dynamics (although parts A and B are useful, too, these can be skipped).
IPhO-1995-Pr2 - a somewhat mathematical problem on geometrical optics (for sound), with an interesting physics.
IPhO-1998-Pr3 - a simple relativistic analysis of a nice astrophysical effect.
IPhO-2003-Pr3-PartA - a challenging problem on relativistic dynamics requiring either a lot of experience, or a flash of inspiration.
IPhO-2016-Pr3 A good exercise on relativistic dynamics; with part A6 you will learn, once again, that in relativity, you should use momentum instead of speed.
IPhO-2018-Pr2 - ATLAS detector - exercises on relativistic dynamics.
From APhO-s:
APhO-2007-Pr1-PartA - a nice problem on negative coefficient of refraction.
APhO-2007-Pr3-PartB - an exercise for mastering relativistic dynamics (inverse Compton scattering).
APhO-2014-Pr3 - on gravitational lenses.
Physics Cup:
Physics Cup 2012 - Pr7 - a really challenging problem on geometrical optics (constructions).
Physics Cup 2012 - Pr9 - on relativistic inelastic scattering - turned out to be the simplest problem of Physics Cup.
Physics Cup 2017 - Pr4 - another challenging problem on geometrical optics constructions.
Physics Cup 2018 - Pr2 - relativistic space ships: ict-diagram is sometimes really useful.

From Estonian-Finnish Olympiads:
Est-Fin-2006-Pr2 - tests your insight to the geometrical optics.
Est-Fin-2012-Pr6 - a problem abut uranium decay and heat balance.
Est-Fin-2013-Pr9 - another problem for testing your skills in geometrical optics.

Estonian homepage of IPhO FORMULAS for IPhOs Send a comment