Collection of Problems
Collection of Problems
The following is a list of problems from previous olympiads, sorted by topic. The rating illustrates how instructive the problem is, and the length refers to how long solving it takes. Hard problems aren't necessarily long and vice versa! Keep in mind that these ratings are subjective. One may find an 'easy' problem to be extremely challenging while a 'hard' problem to be trivial.
Here is an arguably exhaustive list of viable problems, covering most topics that will show up on the actual IPhO competition.
Astrophysics: IOAA past paper, solution, and a problem book (2014-21) ; CAAO lecture notes ; GeCAA past paper ;
Geogebra – draw physics diagrams
Mathematica – good for analytical calculations
MATLAB – good for numerical calculations
OOMMF – micromagnetic simulations
Mechanics
Classical Mechanics (Goldstein)
Lecture Notes on Classical Mechanics (Golwala)
Analytical Mechanics (Hand)
An Introduction to Mechanics (Kleppner)
Mechanics The Classical Theory of Fields (Landau)
Introductory Classical Mechanics (Morin)
Classical Dynamics of Particles and Systems (Thornton)
Electromagnetism
Classical Electrodynamics (Jackson)
Electricity and Magnetism Notes (MIT)
Thermodynamics
Statistical Physics of Particles (Kardar)
Treatise on Thermodynamics (Planck)
Quantum Mechanics
Quantum Mechanics: A Modern Development (Ballentine)
Principles of Quantum Mechanics (Shankar) –> Solutions
General
Introductory Physics I Introductory Physics II (Brown)
Feynman Lectures (Feynman)
The Character of Physical Law (Feynman)
Fundamentals of Physics (Halliday)
College Physics (Serway)
The Theoretical Minimum (Susskind)
David Tong: Lectures on Theoretical Physics (Tong)
University Physics with Modern Physics (Young)
Problems
A Guide to Physics Problems: Part 1 (Cahn)
200 Puzzling Physics Problems (Gnadig)
Problems in General Physics (Irodov)
1000 Solved Problems in Classical Physics (Kamal)
Problem of the Week (Morin)
Other
Elements of Astrophysics (Kaiser)
Problems and Solutions of Atomic, Nuclear, and Particle Physics (Lim)
An Introduction to Error Analysis (Taylor)
Mathematics
Elementary Differential Equations and Boundary Value Problems (Boyce)
Introduction to Differential Equations (Chasnov)
Differential Equations for Dummies (Holzner)
Linear Algebra and Its Applications (Lay)
PROBLEM NAME
RATING
DIFFICULTY
LENGTH
DESCRIPTION
IPhO 2012 T1
2
2
2
Minimization: Minimizing the path of a projectile moving through a sphere.
Physics Cup 2012 P1
3
3
2
TBA
Physics Cup 2019 P3
2
3
3
TBA
EuPhO 2019 T3
3
3
1
TBA
PROBLEM NAME
RATING
DIFFICULTY
LENGTH
DESCRIPTION
NBPhO 2019 P7
2
2
1
Dominoes on Stairs: Calculating the terminal speed of falling dominos.
IPhO 2003 P1
2
4
4
A Swing with a Falling Weight: Analysis of a swing's rotational motion in various situations
NBPhO 2017 P4
3
2
1
Gravitational Waves: Estimating locations of binary black boles by modelling stress and strain
USAPhO 2018 B3
3
1
2
Poynting–Robertson Effect: Developing a simple model for the time for Dust Particles to be cleared of orbit
INPhO 2020 P5
3
2
2
Bullet in a Rod: A relatively standard but good practice for problems on rotational collision
CPhO 2018 P3
2
3
4
Rotating rod collision: Using conservation laws and newton's force equations to analyse the motion of a rod under gravity when a projectile embeds in it
IPhO 1995 T3
3
2
2
Cylindrical Buoy: Modelling pertubations in a buoy floating on sea-water
USAPhO 2019 B3
3
2
2
Pitfall: A good exercise using all areas of Classical mechanics to analyse the motion of a falling constrained rod with masses at its ends
APhO 2010 T1
1
1
1
TBA
GPhO 2016 T1
2
2
2
Stabilizing unstable states: A good exercise on rotational motion and provides insight into the working of Kapitza's pendulum
USAPhO 2017 B1
3
2
2
Dominoes on Table : Toppling of dominoes; Energy lost in collision; Propagation speed of falling Dominoes.
USAPhO 2017 A1
2
1
1
Two Wedges : Statics problem on two Wedges. Can be solved elegantly using geometry.
EuPhO 2020 T2
4
3
1
TBA
PROBLEM NAME
RATING
DIFFICULTY
LENGTH
DESCRIPTION
USAPhO 2012 B2
2
2
2
Magnetic Monopole: Generalizing Gauss's Law to apply on hyopthetical magnetic monopoles. Introduces neat techniques to calculate flux.
INPhO 2015 P2
2
2
2
Elestrostatic Shielding: Understanding the nature of electrostatic forces on uncharged spherical confuctor by point charges in various situations
INPhO 2020 P2
2
1
1
The Feynman Disk Paradox: Analogous to the well known disk paradox; Analyzes the torque produced due to electromagnetic induction in charged cylinder
CPhO 2018 P4
3
4
4
Ioffe-Pritchard Magnetic Trap: Model of a famous magnetic trap used to trap atoms and uses calculation of magnetic fields and binding energy requiring clever approximation skills
IPhO 2010 T1
3
2
3
Image Charges: An excellent problem for practice on image charges. The problem requires having clear fundamentals of elestrostatics of conductors.
Physics Cup 2020 P1
1
1
1
TBA
Physics Cup 2017 P1
4
4
4
Interaction Force: Estimating the interaction force between a point charge and a circular metallic disc kept far away using differential form of Gauss' Law and vector calculus amongst other higher order integration techniques.
INPhO 2011 P1
2
2
2
Electron Escaping a Wire: An excellent problem describing the parameters in an electron escaping a wire. The problem requires good knowledge of vector components and fundamentals to solve.
IPhO 1994 P2
3
3
3
-
APhO 2012 T1
3
3
3
-
PROBLEM NAME
RATING
DIFFICULTY
LENGTH
DESCRIPTION
USAPhO 2011 A4
3
1
1
Stefan Boltzmann Law: Using a simplified model of electromagnetic radiation and quantum mechanics to derive the famous law.
INPhO 2013 P7
3
3
3
Brunt-Väisälä Frequency: Using a model of a balloon in the atmosphere executing Brunt-Väisälä oscillations
USAAO 2019 P7
3
2
2
Black Hole Physics: A nice stellar physics problem which provides a crude model of black holes using Chandrashekar limit and Hawking's temperature
INPhO 2005 P11
4
3
3
Birth of a Star: Estimating the minimum mass a gaseous hydrogen cloud contracting under gravity should have to become a star taking into account Pauli's electron degeneracy pressure. Has many real life applications.
IPhO 2014 T2
3
3
4
Van Der Waals: Analysis of non-ideal gas using Van Der Waals model and application of different concepts like surface tension using it
IPhO 1997 T1
2
2
2
Mountain Physics: Analyzing the movement of moist air masses moving on through a mountain.
IPhO 1992 T3
3
2
2
Satellite in Sunshine: A brilliant mix of conceptual and calculative analysis on Planck's radiation law and the Stefan-Boltzmann's law
USAPhO 2019 A2
3
2
2
Green Revolution: Investigating a simple thermodynamic model for the conversion of solar energy into wind.
APhO 2012 T3
4
3
3
-
Physics Cup 2018 P5
4
5
4
-
APhO 2010 T3
4
3
4
-
IPhO 1989 T1
2
2
3
-
NBPhO 2014 T9
4
3
3
-
PROBLEM NAME
RATING
DIFFICULTY
LENGTH
DESCRIPTION
USAPhO 2018 B2
1
1
1
Telescope Mirror: Using the Uncertainty Principle to Estimate Size of Telescope to Observe Distant Stars
INPhO 2020 P4
3
2
2
Source in Circular Motion: A lovely problem requiring detective-like casework on the various possibilities of the position of wave detectors
NBPhO 2012 P1
3
2
2
-
IPhO 1995 T2
3
3
3
-
IPhO 2015 T2(b)
4
3
2
-
Physics Cup 2012 P0
2
3
2
-
NBPhO 2019 P5
3
2
2
-
EuPhO 2020 T3
4
4
3
-
PROBLEM NAME
RATING
DIFFICULTY
LENGTH
DESCRIPTION
USAPhO 2017 A4
2
1
1
Relativistic Collision: Introduces a clever technique to model the collision between two subatomic praticles at relativistic speeds and also talks briefly about Cosmic Microwave Background Radiation
INPhO 2020 P3
2
1
2
Two-Electron Bohr Model: Creating a new Bohr Model for a two-electron system revolving around a nucleus
Physics Cup 2012 P9
3
3
3
Particle Collisions: A problem on an electron that is given electrical power to collide with a positron to produce gamma rays.