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,
Mechanics (incl. celestial mechanics)
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. 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.
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-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.
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.
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.
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).
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.
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.
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.
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).
Wave optics and quantum mechanics
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.
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).
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-1999-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.