Physics Collection

Advanced Physics and Physics Olympiad Training Materials

I trained the HCI Physics Olympiad team from 2023—2024,
and also lectured for the Singapore Physics Olympiad Training in 2024.
Currently, I am in an advisory role helping with the new HCI PhO trainers
in their work in addition to helping some students in private tutoring.

Here are some materials which I make publicly available in case they may be of use to someone. :)

Latest Materials (2025)

Instructions (LINK)

Problem Set 1 (LINK)

Problem Set 2 (LINK)

Problem Set 3 (LINK)

Below, I provide problem sets useful for the training of a student to perform at the SPhO level (also roughly equivalent to other countries’ national Olympiads).

These materials were produced for one of my students as part of the training specific to him, tailored to his strengths and weaknesses. Therefore, the level of these materials may not be perfectly suited for everyone. Nevertheless, I hope that if you’ve found your way here and you are a PhO student, you may find them helpful.

These materials will be suitable for you if: (1) You already have a strong foundation in the basic concepts of classical mechanics and beyond, at the level of SJPO Silver or Gold medal. (2) You have a strong mathematical foundation consisting of at least A Level calculus, vectors, and differential equations. (3) You have a strong analytical problem-solving mind, and are able to work through difficult problems on your own and think deeply about how to get unstuck when you may face difficulties.

If you do not meet criterion (1) and are interested in preparing for the SPhO, please consider the standard recommendation of Young and Freedman’s University Physics textbook. Read through the content and work through questions enough to get an understanding, then you may return here. If you do not meet criterion (2), consider studying these materials following MIT OCW’s 18.01, 18.02, 18.03 courses, or seeking out various resources on the materials such as Stewart’s Calculus textbook, Khan Academy, or Paul’s Online Math Notes. If you do not meet condition (3), work on both the above recommendations with an emphasis on problem solving.

What is beyond this point is addressed to, and will only be helpful for, students who meet all three criteria.

You should work through the materials with the help of a suitable teacher or senior who is at the APhO/IPhO level or beyond. There are many discussion problems the insights within which can only be brought out when engaging in discussion with an insightful instructor. There are also some questions which are intended to be very difficult, though extremely helpful for learning, and you will most likely only be able to gain the benefits through the explanation of a skilled instructor. If this is not accessible, you should at least work through the materials with a friend (or multiple friends) at a similar level and bounce ideas off each other to make progress. After each question, ensure that you review to see what the point of the question was — what have you learnt from it? Consolidating this view after each question is extremely important for retention and deep learning.

The questions are designed with learning in mind; every question is there for a purpose. These are not just questions for mindless grinding; they are materials for purposeful learning. I wish you make the most of it.

In this document, I give brief instructions about how to make correct use of the problem sets.

Problem Set 1 is about Mathematical Foundations necessary for Physics Olympiad. You are assumed to already be familiar with the concepts of calculus, vectors, and differential equations, and have a rough sense of how they are applied in physics. This problem set is mainly about exposing you to applications of this mathematics in the physicist’s world. If you find the questions too difficult, either review A Level mathematics or Young and Freedman, depending on the nature of your troubles (is it more about the math or the application?).

Problem Set 2 is about Force Analysis in Newtonian mechanics. You are assumed to already be familiar with basic force analysis questions at the level of Young and Freedman; this problem set emphasises more advanced questions such as those requiring differential analysis. If you find the questions too difficult, go back to Young and Freedman (easiest), or Morin’s Problems and Solutions in Introductory Mechanics (easier), or Morin’s Introduction to Classical Mechanics with Problems and Solutions (harder).

Problem Set 3 is about Energy and Momentum in Newtonian mechanics. You are assumed to already be familiar with the concepts at a basic level, as well as having some understanding and familiarity with derivations of important theorems, and the use of conservation of energy and momentum to solve problems like collisions. If this is not the case, and you find the questions too difficult, go back to Young and Freedman or the two Morin books recommended above.

More materials are to come. A new problem set will be added roughly every 3 weeks.

Older Materials (2024 and before)