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IPhO Problem-Solving Framework (Beginner-Friendly)

Beginner-friendly IPhO problem-solving framework: modelling statements, method selection, approximation discipline, and sanity checks.

  • International Physics Olympiad preparation

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On this page

IPhO problems feel “hard” because they test process, not memorised formulas. This page is a beginner-friendly framework you can reuse for any olympiad-style question, including experimental write-ups.

Who this is for

This is for students who are roughly A Level-competent but new to IPhO style. If basics are missing, start from:

1. Definitions (Must Know)

  • Model: your simplified physics story of the system (coordinates, constraints, forces/energies, and the equation you will solve).
  • Assumption / idealisation: changes the model class (point mass, rigid rod, massless string, no air drag).
  • Approximation: drops smaller terms inside a chosen model, justified by a small parameter like ε ≪ 1.
  • Method marks: marks for correct setup (diagram, equations, assumptions), even if algebra later is messy.
  • Sanity check: a quick check that catches 80 percent of errors (units, sign, limit cases, scaling).

2. The 8-Step Workflow (Scaffold)

Use this as your default routine
  1. Draw a diagram and define your symbols.
  2. Write a 2 to 4 line modelling statement (system, coordinates, assumptions).
  3. Decide the “big tool” (energy, momentum, angular momentum, Gauss/Ampere, first law, etc.).
  4. Write the core equation(s) cleanly (before any substitution).
  5. Reduce variables using constraints/symmetry.
  6. Only then do algebra (keep it structured, not a wall of steps).
  7. Do 2 sanity checks (units + one limit).
  8. Write a final answer sentence with units (and uncertainty if experimental).

3. Beginner Explanations (Why Each Step Matters)

3.1 The modelling statement (the most underrated skill)

Many “hard” IPhO problems become easy once you commit to a model early.

Your modelling statement should contain:

  • system + boundary: what is inside and outside
  • coordinates + sign: what you will solve for
  • assumptions + one justification: a ratio or a scale estimate
Template: a 3-line modelling statement (copy-paste style)
  1. “We treat ___ as ___ and choose coordinate(s) ___ with positive direction ___.”
  2. “Assume ___ because ___ (small ratio / scale estimate). Neglect ___.”
  3. “We will check units and the limits ___ and ___.”

3.2 Method choice: how to decide in 15 seconds

Ask: “Which quantity is hardest to compute directly?” Then choose a method that avoids it.

Examples:

  • forces are messy but constraints are clean: use energy or Lagrangian
  • collision is short: use impulse/momentum
  • rotation around a point: use angular momentum or torque about a smart point
  • field geometry: use symmetry + Gauss/Ampere, not integration
  • heat/work bookkeeping: use first law with a clear system and sign convention
A good method choice sounds like this

“I won’t compute tension directly. I’ll write energy with the rolling constraint v = ω R.”

“I won’t compute the full field. I’ll use symmetry to show the direction and then choose a Gaussian surface.”

3.3 Approximations without hand-waving

You do not get full credit for “ignore air resistance” unless you justify it.

You want a dimensionless ratio like:

F_drag/mg ∼ 10⁻² ≪ 1

or

h/R_⊕ ≪ 1.

If you cannot find a ratio, do not pretend the approximation is justified. Either keep the term, or state it as an assumption explicitly.

3.4 Sanity checks that catch most mistakes

Do these at the end of every problem:

  • units: does each term have the same unit? does the final answer unit match the asked quantity?
  • limits: what happens if a parameter goes to 0 or becomes very large?
  • sign and direction: does the result point the right way?
  • scaling: if you double the length scale, does the result change in the expected direction?

4. Common Beginner Mistakes (And Fixes)

  • Starting algebra before defining coordinates and sign conventions.
  • Solving the wrong variable (because symbols were never defined).
  • Carrying 6 variables when a constraint could reduce it to 1.
  • Using the right equation in the wrong place (Bernoulli across a pump, Gauss without symmetry).
  • Ending with a number but no units and no final sentence.

5. Exam Tips (High ROI)

  1. Put the modelling statement near the start. Markers award structure.
  2. Keep equations “one per line” and label them if there are several.
  3. If a result is messy, box the final form clearly and explain what it means.
  4. For experiments: always state one dominant systematic error and its direction of effect.

6. Worked Examples (use Toggle)

1) Example outline: rolling down an incline (energy + constraint)

Goal: find acceleration of a rigid cylinder rolling without slipping down an incline.

Modelling statement:

  • Treat the cylinder as a rigid body of mass m and radius R.
  • Assume pure rolling (no slip) so v = ω R.
  • Neglect air drag and rolling resistance.

Method choice: use energy (static friction does no work at the contact point for pure rolling on a stationary surface).

Energy drop after moving distance s along an incline of angle α:

mgs sin α = 1/2 mv² + 1/2 Iω².

Use ω = v/R:

mgs sin α = 1/2 mv²(1 + I/mR²).

Differentiate with respect to time or use v² = 2as to get

a = (g sin α)/(1 + I/(mR²)).

Sanity checks:

  • if I → 0 (point mass), a → g sin α
  • larger I gives smaller a (more energy into rotation)
2) Example outline: RC transient (time scale first)

Goal: find how the capacitor voltage changes after a switch is closed.

Modelling statement:

  • Use ideal components.
  • Capacitor current: I = C dV_C/dt.
  • Resistor drop: V_R = IR.

Method choice: write the one ODE for V_C.

For charging from a source V₀ through R:

V₀ = V_R + V_C = RCdV_C/dt + V_C.

Solution form:

V_C(t) = V₀(1 - e^(-t/RC)).

Sanity checks:

  • at t = 0, V_C = 0
  • as t → ∞, V_C → V₀
  • the time constant is τ = RC

7. Mind Stretchers (use Toggle)

1) Debugging: what do you do when you are stuck after 10 minutes?

Try this sequence:

  1. Re-draw the diagram with fewer elements and re-define symbols.
  2. Ask “what is conserved?” (energy, momentum, charge, entropy, etc.).
  3. Estimate scales: write a one-line order-of-magnitude to see which terms matter.
  4. Look for a constraint that reduces variables (geometry, rolling, incompressibility, symmetry).
  5. If still stuck, switch method: energy to momentum, forces to Lagrangian, field integration to symmetry arguments.

8. Practice (Do This Before Problem Sets)

Your starter training loop (beginner-friendly)
  1. Do the foundations path below.
  2. Attempt one problem from a hub’s problem set (timed).
  3. Write a 3-line modelling statement you wish you started with.
  4. Re-solve the problem 48 hours later without notes.

Foundations (Start Here)

  • Problem-Solving Framework (Beginner-Friendly)

    A reusable checklist: modelling, method choice, approximations, checks.

    Open lesson

  • Modelling & Approximations

    How to simplify without losing the physics.

    Open lesson

  • Scaling & Dimensional Analysis

    Nondimensionalise, spot balances, and bound errors.

    Open lesson

  • Electrostatics with Symmetry

    Choose surfaces/arguments where symmetry collapses the algebra.

    Open lesson

  • First Law Problem Patterns

    System definition, signs, and fast bookkeeping.

    Open lesson

  • Phasors & Superposition

    Add oscillations fast and track phase reliably.

    Open lesson

  • Special Relativity Toolkit

    Invariants, frames, and fast consistency checks.

    Open lesson

  • Uncertainty & Error Propagation

    Uncertainty habits for experimental marks and clean conclusions.

    Open lesson

Mind-stretcher feedback

  • The order-of-magnitude line should compare the sizes of competing terms before detailed algebra. A defensible estimate states the scale, ratio and resulting approximation; it does not delete a term merely because its expression looks complicated.
Syllabus and review details

No official syllabus alignment is listed for this lesson.