## 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.
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.

### Electromagnetism

##### 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.
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.

### Thermodynamics

##### 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.
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!
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.