Physics Olympiad · Vol I

Olympiad in 52 chapters — from “Dimensional analysis” to “Capstone”.

Chapters

  1. Dimensional analysis
    • A1.1Why dimensional analysis works
    • A1.2What it feels like, in practice
    • A1.3The method, walked through
    • A1.4Five signatures, with quick cases
    • A1.5Where dimensional analysis fails
    • A1.6Getting the prefactor
    • A1.7Drills
    • A1.8Your Edge after this chapter
    • A1.9Bridge to the next chapter
  2. Small parameters
    • A2.1Why expansion works
    • A2.2What it feels like, in practice
    • A2.3The method, walked through
    • A2.4Five signatures, with quick cases
    • A2.5Where expansion fails
    • A2.6Getting the next-order correction
    • A2.7Drills
    • A2.8Your Edge after this chapter
    • A2.9Bridge to the next chapter
  3. Vectors and index notation
    • A3.1Why index notation wins
    • A3.2What it feels like, in practice
    • A3.3The method, walked through
    • A3.4Four identities you will use in every chapter
    • A3.5Where it fails
    • A3.6Drills
    • A3.7Your Edge after this chapter
    • A3.8Bridge to the next chapter
  4. Complex numbers and Fourier
    • A4.1Why complex numbers win
    • A4.2What it feels like, in practice
    • A4.3The method, walked through
    • A4.4Four signatures, with quick cases
    • A4.5Where it fails
    • A4.6Drills
    • A4.7Your Edge after this chapter
    • A4.8Bridge to the next chapter
  5. Kinematics
    • B1.1Why frame choice matters
    • B1.2What it feels like, in practice
    • B1.3The method, walked through
    • B1.4Four signatures, with quick cases
    • B1.5Where it fails (pseudo-forces and their price)
    • B1.6Drills
    • B1.7Your Edge after this chapter
    • B1.8Bridge to the next chapter
  6. Newton’s laws
    • B2.1Newton’s laws, revisited
    • B2.2What it feels like, in practice
    • B2.3The method, walked through
    • B2.4Three signatures, with quick cases
    • B2.5Where it fails
    • B2.6Drills
    • B2.7Your Edge after this chapter
    • B2.8Bridge to the next chapter
  7. Momentum and impulse
    • B3.1Why momentum conservation works
    • B3.2What it feels like, in practice
    • B3.3Variable-mass systems
    • B3.4Three signatures, with quick cases
    • B3.5Where it fails
    • B3.6Drills
    • B3.7Your Edge after this chapter
    • B3.8Bridge to the next chapter
  8. Energy methods
    • B4.1Why energy is conserved
    • B4.2What it feels like, in practice
    • B4.3The method, walked through
    • B4.4Four signatures, with quick cases
    • B4.5Where it fails
    • B4.6Drills
    • B4.7Your Edge after this chapter
    • B4.8Bridge to the next chapter
  9. Central forces
    • B5.1Why central forces are special
    • B5.2What it feels like, in practice
    • B5.3The method, walked through: Kepler orbits
    • B5.4Four signatures, with quick cases
    • B5.5Where it fails
    • B5.6Drills
    • B5.7Your Edge after this chapter
    • B5.8Bridge to the next chapter
  10. Rotation
    • C1.1Why the inertia tensor simplifies rotation
    • C1.2What it feels like, in practice
    • C1.3The two axis theorems, walked through
    • C1.4Four signatures, with quick cases
    • C1.5Where it fails
    • C1.6Drills
    • C1.7Your Edge after this chapter
    • C1.8Bridge to the next chapter
  11. Torques and precession
    • C2.1Torque as angular momentum change
    • C2.2What it feels like, in practice
    • C2.3Deriving the precession frequency
    • C2.4Three signatures, with quick cases
    • C2.5Where it fails
    • C2.6Drills
    • C2.7Your Edge after this chapter
    • C2.8Bridge to the next chapter
  12. Continua
    • C3.1Pressure, stress, and cut-and-balance
    • C3.2What it feels like, in practice
    • C3.3Hydrostatic pressure and buoyancy, walked through
    • C3.4Three signatures, with quick cases
    • C3.5Where it fails
    • C3.6Drills
    • C3.7Your Edge after this chapter
    • C3.8Bridge to the next chapter
  13. The canonical oscillator
    • D1.1The three damping regimes
    • D1.2What it feels like, in practice
    • D1.3Driven damped resonance, walked through
    • D1.4Four signatures, with quick cases
    • D1.5Where it fails
    • D1.6Drills
    • D1.7Your Edge after this chapter
    • D1.8Bridge to the next chapter
  14. Waves
    • D2.1The wave equation as a continuum limit
    • D2.2What it feels like, in practice
    • D2.3Standing waves on a string, walked through
    • D2.4Four signatures, with quick cases
    • D2.5Where it fails
    • D2.6Drills
    • D2.7Your Edge after this chapter
    • D2.8Bridge to the next chapter
  15. Non-linear oscillation
    • D3.1Why non-linear is different
    • D3.2What it feels like, in practice
    • D3.3Parametric resonance, walked through
    • D3.4Three signatures, with quick cases
    • D3.5Where it fails (and where it becomes chaos)
    • D3.6Drills
    • D3.7Your Edge after this chapter
    • D3.8Bridge to the next chapter
  16. Fluid dynamics
    • D4.1Bernoulli and Reynolds
    • D4.2What it feels like, in practice
    • D4.3Flow through a constriction, walked through
    • D4.4Three signatures, with quick cases
    • D4.5Where it fails
    • D4.6Drills
    • D4.7Your Edge after this chapter
    • D4.8Bridge to the next chapter
  17. Lagrangian mechanics
    • E1.1The Lagrangian and Euler-Lagrange equations
    • E1.2What it feels like, in practice
    • E1.3The double pendulum, walked through
    • E1.4Three signatures, with quick cases
    • E1.5Where it fails
    • E1.6Drills
    • E1.7Your Edge after this chapter
    • E1.8Bridge to the next chapter
  18. Hamiltonian mechanics
    • E2.1The Hamiltonian and phase space
    • E2.2What it feels like, in practice
    • E2.3Adiabatic invariants for a pendulum, walked through
    • E2.4Three signatures, with quick cases
    • E2.5Where it fails
    • E2.6Drills
    • E2.7Your Edge after this chapter
    • E2.8Bridge to Volume II
  19. Charges, fields, Gauss
    • F1.1Coulomb, the field, and Gauss
    • F1.2What it feels like, in practice
    • F1.3Field of a uniformly charged sphere, walked through
    • F1.4Four signatures, with quick cases
    • F1.5Where it fails
    • F1.6Drills
    • F1.7Your Edge after this chapter
    • F1.8Bridge to the next chapter
  20. Potentials and multipoles
    • F2.1The scalar potential
    • F2.2What it feels like, in practice
    • F2.3Multipole expansion, walked through
    • F2.4Three signatures, with quick cases
    • F2.5Where it fails
    • F2.6Drills
    • F2.7Your Edge after this chapter
    • F2.8Bridge to the next chapter
  21. Conductors, capacitance, dielectrics
    • F3.1Conductors in equilibrium
    • F3.2What it feels like, in practice
    • F3.3Method of images, walked through
    • F3.4Dielectrics
    • F3.5Three signatures, with quick cases
    • F3.6Where it fails
    • F3.7Drills
    • F3.8Your Edge after this chapter
    • F3.9Bridge to the next chapter
  22. Currents and magnetic fields
    • F4.1Biot-Savart and Ampère
    • F4.2What it feels like, in practice
    • F4.3The method, walked through: long wire and solenoid
    • F4.4Three signatures, with quick cases
    • F4.5Where it fails
    • F4.6Drills
    • F4.7Your Edge after this chapter
    • F4.8Bridge to the next chapter
  23. Faraday and induction
    • G1.1Faraday’s law
    • G1.2What it feels like, in practice
    • G1.3Motional EMF in a sliding bar, walked through
    • G1.4Four signatures, with quick cases
    • G1.5Where it fails
    • G1.6Drills
    • G1.7Your Edge after this chapter
    • G1.8Bridge to the next chapter
  24. Maxwell’s equations
    • G2.1The four equations
    • G2.2The wave equation in vacuum
    • G2.3Three signatures, with quick cases
    • G2.4Where it fails
    • G2.5Drills
    • G2.6Your Edge after this chapter
    • G2.7Bridge to the next chapter
  25. EM waves
    • G3.1Plane waves and polarisation
    • G3.2What it feels like, in practice
    • G3.3The Poynting vector, walked through
    • G3.4Three signatures, with quick cases
    • G3.5Where it fails
    • G3.6Drills
    • G3.7Your Edge after this chapter
    • G3.8Bridge to the next chapter
  26. DC circuits
    • H1.1Ohm and Kirchhoff
    • H1.2What it feels like, in practice
    • H1.3Wheatstone bridge and symmetry, walked through
    • H1.4Three signatures, with quick cases
    • H1.5Where it fails
    • H1.6Drills
    • H1.7Your Edge after this chapter
    • H1.8Bridge to the next chapter
  27. Transients and AC
    • H2.1Complex impedance
    • H2.2What it feels like, in practice
    • H2.3RLC resonance, walked through
    • H2.4Three signatures, with quick cases
    • H2.5Where it fails
    • H2.6Drills
    • H2.7Your Edge after this chapter
    • H2.8Bridge to the next chapter
  28. Geometric optics
    • I1.1Fermat, Snell, and rays
    • I1.2The thin-lens equation, walked through
    • I1.3Three signatures, with quick cases
    • I1.4Where it fails
    • I1.5Drills
    • I1.6Your Edge after this chapter
    • I1.7Bridge to the next chapter
  29. Wave optics
    • I2.1Coherence and phasor sums
    • I2.2Double-slit and grating, walked through
    • I2.3Three signatures, with quick cases
    • I2.4Where it fails
    • I2.5Drills
    • I2.6Your Edge after this chapter
    • I2.7Bridge to the next chapter
  30. Polarisation and the photon limit
    • I3.1Polarisation and Malus
    • I3.2Brewster’s angle, walked through
    • I3.3The photon limit
    • I3.4Three signatures, with quick cases
    • I3.5Where it fails
    • I3.6Drills
    • I3.7Your Edge after this chapter
    • I3.8Bridge to the next chapter
  31. Temperature, heat, the first law
    • J1.1Temperature and the ideal gas law
    • J1.2Canonical processes, walked through
    • J1.3Three signatures, with quick cases
    • J1.4Where it fails
    • J1.5Drills
    • J1.6Your Edge after this chapter
    • J1.7Bridge to the next chapter
  32. The second law
    • J2.1Entropy and the second law
    • J2.2The Carnot cycle, walked through
    • J2.3Three signatures, with quick cases
    • J2.4Where it fails
    • J2.5Drills
    • J2.6Your Edge after this chapter
    • J2.7Bridge to the next chapter
  33. Engines and thermodynamic potentials
    • J3.1Cycles on PV diagrams
    • J3.2Thermodynamic potentials
    • J3.3Three signatures, with quick cases
    • J3.4Where it fails
    • J3.5Drills
    • J3.6Your Edge after this chapter
    • J3.7Bridge to the next chapter
  34. Kinetic theory
    • J4.1Pressure from collisions
    • J4.2Maxwell-Boltzmann distribution
    • J4.3Mean free path
    • J4.4Three signatures, with quick cases
    • J4.5Where it fails
    • J4.6Drills
    • J4.7Your Edge after this chapter
    • J4.8Bridge to the next chapter
  35. Boltzmann and the partition function
    • J5.1The Boltzmann distribution
    • J5.2What it feels like, in practice
    • J5.3Three signatures, with quick cases
    • J5.4Where it fails
    • J5.5Drills
    • J5.6Your Edge after this chapter
    • J5.7Bridge to the next chapter
  36. Phase transitions
    • J6.1First-order and second-order transitions
    • J6.2Three signatures, with quick cases
    • J6.3Where it fails
    • J6.4Drills
    • J6.5Your Edge after this chapter
    • J6.6Bridge to the next chapter
  37. Black-body radiation
    • J7.1Planck’s spectrum
    • J7.2Three signatures, with quick cases
    • J7.3Where it fails
    • J7.4Drills
    • J7.5Your Edge after this chapter
    • J7.6Bridge to Volume III
  38. Special relativity
    • K1.1Postulates and Lorentz transformations
    • K1.2Time dilation and length contraction
    • K1.3Three signatures, with quick cases
    • K1.4Where it fails
    • K1.5Drills
    • K1.6Your Edge after this chapter
    • K1.7Bridge to the next chapter
  39. Relativistic dynamics
    • K2.1Four-vectors and four-momentum
    • K2.2Particle decay and threshold reactions
    • K2.3Three signatures, with quick cases
    • K2.4Where it fails
    • K2.5Drills
    • K2.6Your Edge after this chapter
    • K2.7Bridge to the next chapter
  40. General relativity
    • K3.1The equivalence principle
    • K3.2Three signatures, with quick cases
    • K3.3Where it fails
    • K3.4Drills
    • K3.5Your Edge after this chapter
    • K3.6Bridge to the next chapter
  41. Old quantum and wave mechanics
    • L1.1The old quantum theory
    • L1.2The Schrödinger equation (1D)
    • L1.3Three signatures, with quick cases
    • L1.4Where it fails
    • L1.5Drills
    • L1.6Your Edge after this chapter
    • L1.7Bridge to the next chapter
  42. Atoms and spectra
    • L2.1The hydrogen atom
    • L2.2Three signatures, with quick cases
    • L2.3Where it fails
    • L2.4Drills
    • L2.5Your Edge after this chapter
    • L2.6Bridge to the next chapter
  43. Quantum statistics
    • L3.1Fermi-Dirac and Bose-Einstein
    • L3.2Three signatures, with quick cases
    • L3.3Where it fails
    • L3.4Drills
    • L3.5Your Edge after this chapter
    • L3.6Bridge to the next chapter
  44. Error analysis and data fitting
    • M1.1Random and systematic errors
    • M1.2Linear regression
    • M1.3Three signatures, with quick cases
    • M1.4Where it fails
    • M1.5Drills
    • M1.6Your Edge after this chapter
    • M1.7Bridge to the next chapter
  45. Mechanics lab
    • M2.1Four mechanics experiments
    • M2.2Where these fail
    • M2.3Drills
    • M2.4Your Edge after this chapter
    • M2.5Bridge to the next chapter
  46. Electrical lab
    • M3.1Instruments and their limitations
    • M3.2Four electrical experiments
    • M3.3Where these fail
    • M3.4Drills
    • M3.5Your Edge after this chapter
    • M3.6Bridge to the next chapter
  47. Optical lab
    • M4.1Interferometric measurement
    • M4.2Photodetectors
    • M4.3Where these fail
    • M4.4Drills
    • M4.5Your Edge after this chapter
    • M4.6Bridge to the next chapter
  48. Thermal and modern-physics lab
    • M5.1Four canonical experiments
    • M5.2Where these fail
    • M5.3Drills
    • M5.4Your Edge after this chapter
    • M5.5Bridge to the next chapter
  49. The technique taxonomy
    • N1.1Techniques (the named methods)
    • N1.2Insights (the realisations that unlock problem classes)
    • N1.3Shortcuts (the tactical moves)
    • N1.4How to use this index
    • N1.5Bridge to the next chapter
  50. IPhO theoretical paper
    • N2.1Time budget
    • N2.2Solving tactics
    • N2.3Presentation
    • N2.4Failure modes
    • N2.5Bridge to the next chapter
  51. IPhO experimental paper
    • N3.1Time budget
    • N3.2Apparatus inspection
    • N3.3Data taking
    • N3.4Analysis and write-up
    • N3.5Failure modes
    • N3.6Bridge to the next chapter
  52. Capstone
    • N4.1Problem 1: A chain falling off a table
    • N4.2Problem 2: Magnetic braking of a ring
    • N4.3Problem 3: Photon emission and recoil from an atom at rest
    • N4.4Closing