IPhO Mechanics Problem Set (Official Problems + Hints)
Curated IPhO mechanics problems (theory + experimental) grouped by technique, with solution outlines and common traps.
On this page
This set is for mechanics problems where modelling, constraints, and method choice matter more than algebra.
If you have not done the hub path yet, start with the IPhO Mechanics Hub.
These are official IPhO problems linked via a public archive mirror: https://phoxiv.org/contests/ipho
If a link fails, use the IPhO official documentations page and navigate by year: https://www.ipho-new.org/documentations/
Read the framework once: IPhO Problem-Solving Framework
Do the hub Entry and Core lessons first (then return here):
- Start with sections A and B below (starter problems).
- Finish the hub lessons, then do sections C and D (core).
- Do section E (experimental) once per week.
Show the full hub lesson path (Mechanics | IPhO Prep)
A. Constraints, Friction, and Smart Modelling
Outline pattern: constraints and friction without guessing
- choose a generalized coordinate that respects the constraint (reduce variables early) - write one clean free-body diagram and one clean kinematics constraint - use energy when friction is static and the surface point is at rest (check the condition) - for kinetic friction or anisotropic friction, identify the direction of relative motion first - finish with a limit check (zero friction, infinite friction, small angle, large mass ratio)
B. Oscillations and “Effective” Parameters
- IPhO 2019 T1 — “Zero-length springs and slinky coils” (PDF)
Outline pattern: small oscillations in one page
- identify equilibrium and expand the relevant force/energy to second order - write an equation of motion in the form x double dot + ω² x = 0 - if there are coupled coordinates, look for symmetry coordinates (sum/difference) first
- sanity check: period increases with inertia, decreases with stiffness
C. Central Forces and Orbital Thinking
Outline pattern: orbit problems that do not become a mess
- write the conserved quantities first: energy and angular momentum - reduce to 1D radial motion using an effective potential idea (even if you do not name it) - use scale estimates to decide which term dominates in a regime - check limiting cases: circular orbit, escape condition, small eccentricity
D. Fluids, Buoyancy, and “What Sets the Scale?”
- IPhO 2023 T3 — “Water and Objects” (PDF)
Outline pattern: fluids with clean assumptions
- decide early: incompressible or compressible; steady or unsteady; ideal or with losses - write continuity before Bernoulli so you eliminate variables - if forces are asked, use control-volume momentum (momentum flux), not just Bernoulli - include one scaling line to justify neglecting viscosity or turbulence if you do
E. Experimental Mechanics (Write-Up Practice)
Write-up pattern: what to show for marks
- state what you will plot (Y vs X) and what slope/intercept represent - show uncertainty once per column and draw error bars - quote gradient with units and a defensible uncertainty method - finish with: parameter ± uncertainty + 1 dominant systematic + 1 realistic fix
After each attempt, write a 3-line modelling statement you wish you had written at the start. Then continue via the IPhO Mechanics Hub.
Experimental write-up feedback
- Define transformed variables Y and X explicitly, then state what the slope and intercept mean with units. “Plot a graph” without this mapping is incomplete.
- Put one uncertainty convention in each table heading, draw both-axis error bars where relevant, and use extreme acceptable lines rather than bar-by-bar decoration with no inference.