2015-12-06 Syllabus of IPhO
2015-12-06 Syllabus of IPhO
2015-12-06 Syllabus of IPhO
1 Introduction
2.2
2.2.1
Mechanics
Kinematics
Velocity and acceleration of a point particle as the derivaThis syllabus lists topics which may be used for the IPhO.
tives of its displacement vector. Linear speed; centripetal
Guidance about the level of each topic within the syland tangential acceleration. Motion of a point particle
labus is to be found from past IPhO questions.
with a constant acceleration. Addition of velocities and
angular velocities; addition of accelerations without the
1.2 Character of the problems
Coriolis term; recognition of the cases when the Coriolis
acceleration is zero. Motion of a rigid body as a rotaProblems should focus on testing creativity and undertion around an instantaneous centre of rotation; velocistanding of physics rather than testing mathematical virties and accelerations of the material points of rigid rotuosity or speed of working. The proportion of marks altating bodies.
located for mathematical manipulations should be kept
small. In the case of mathematically challenging tasks,
2.2.2 Statics
alternative approximate solutions should receive partial
credit. Problem texts should be concise; the theoreti- Finding the centre of mass of a system via summation
cal and the experimental examination texts should each or via integration. Equilibrium conditions: force balance
contain fewer than 12000 characters (including white (vectorially or in terms of projections), and torque balance (only for one- and two-dimensional geometry). Norspaces, but excluding cover sheets and answer sheets).
mal force, tension force, static and kinetic friction force;
Hookes law, stress, strain, and Young modulus. Stable
1.3 Exceptions
and unstable equilibria.
Questions may contain concepts and phenomena not
mentioned in the Syllabus providing that sucient in- 2.2.3 Dynamics
formation is given in the problem text so that students
Newtons second law (in vector form and via projections
without previous knowledge of these topics would not
(components)); kinetic energy for translational and rotabe at a noticeable disadvantage. Such new concepts must
tional motions. Potential energy for simple force fields
be closely related to the topics included in the syllabus.
(also as a line integral of the force field). Momentum,
Such new concepts should be explained in terms of topangular momentum, energy and their conservation laws.
ics in the Syllabus.
Mechanical work and power; dissipation due to friction.
Inertial and non-inertial frames of reference: inertial
force, centrifugal force, potential energy in a rotating
1.4 Units
frame. Moment of inertia for simple bodies (ring, disk,
Numerical values are to be given using SI units, or units
sphere, hollow sphere, rod), parallel axis theorem; findocially accepted for use with the SI.
ing a moment of inertia via integration.
It is assumed that the contestants are familiar with
the phenomena, concepts, and methods listed below, and 2.2.4 Celestial mechanics
are able to apply their knowledge creatively.
Law of gravity, gravitational potential, Keplers laws (no
derivation needed for first and third law). Energy of a
2 Theoretical skills
point mass on an elliptical orbit.
2.1 General
2.2.5
Hydrodynamics
The ability to make appropriate approximations, while Pressure, buoyancy, continuity law, the Bernoulli equamodelling real life problems. Recognition and ability to tion. Surface tension and the associated energy, capillary pressure.
exploit symmetry in problems.
2.4
2.4.1
Single oscillator
2.4.2
Waves
Propagation of harmonic waves: phase as a linear function of space and time; wave length, wave vector, phase
and group velocities; exponential decay for waves propagating in dissipative media; transverse and longitudinal
waves; the classical Doppler eect. Waves in inhomogeneous media: Fermats principle, Snells law. Sound
waves: speed as a function of pressure (Youngs or bulk
modulus) and density, Mach cone. Energy carried by
waves: proportionality to the square of the amplitude,
2.3.3 Interaction of matter with electric and magnetic
continuity of the energy flux.
fields
2.4.3
Dependence of electric permittivity on frequency (qualitatively); refractive index; dispersion and dissipation of
Linear resistors and Ohms law; Joules law; work done electromagnetic waves in transparent and opaque maby an electromotive force; ideal and non-ideal batter- terials. Linear polarisation; Brewster angle; polarisers;
ies, constant current sources, ammeters, voltmeters and Malus law.
ohmmeters. Nonlinear elements of given V -I characteristic. Capacitors and capacitance (also for a single
2.4.5 Geometrical optics and photometry
electrode with respect to infinity); self-induction and inductance; energy of capacitors and inductors; mutual in- Approximation of geometrical optics: rays and optical
ductance; time constants for RL and RC circuits. AC images; a partial shadow and full shadow. Thin lens apcircuits: complex amplitude; impedance of resistors, in- proximation; construction of images created by ideal thin
ductors, capacitors, and combination circuits; phasor di- lenses; thin lens equation . Luminous flux and its contiagrams; current and voltage resonance; active power.
nuity; illuminance; luminous intensity.
2.3.4 Circuits
2.7.3
Statistical physics
ton scattering. Protons and neutrons as compound particles. Atomic nuclei, energy levels of nuclei (qualitatively); alpha-, beta- and gamma-decays; fission, fusion
and neutron capture; mass defect; half life and exponential decay. photoelectric eect.
The experimental problems may contain implicit theoretical tasks (deriving formulae necessary for calculations); there should be no explicit theoretical tasks unless
these tasks test the understanding of the operation principles of the given experimental setup or of the physics
of the phenomena to be studied, and do not involve long
mathematical calculations.
The expected number of direct measurements and
the volume of numerical calculations should not be so
large as to consume a major part of the allotted time:
the exam should test experimental creativity, rather than
the speed with which the students can perform technical
tasks.
The students should have the following skills.
3.2 Safety
repeated measurements.
Finding absolute and relative uncertainties of a quanKnowing standard safety rules in laboratory work. Nevtity determined as a function of measured quantities usertheless, if the experimental set-up contains any safety
ing any reasonable method (such as linear approximahazards, the appropriate warnings should be included in
tion, addition by modulus or Pythagorean addition).
the text of the problem. Experiments with major safety
hazards should be avoided.
3.6
3.3 Measurement techniques and apparatus
Being familiar with the most common experimental techniques for measuring physical quantities mentioned in
the theoretical part.
Knowing commonly used simple laboratory instruments and digital and analog versions of simple devices, such as calipers, the Vernier scale, stopwatches, thermometers, multimeters (including ohmmeters and AC/DC voltmeters and ammeters), potentiometers, diodes, , lenses, prisms, optical stands, calorimeters,
and so on.
Sophisticated practical equipment likely to be unfamiliar to the students should not dominate a problem. In
the case of moderately sophisticated equipment (such as
oscilloscopes, counters, ratemeters, signal and function
generators, photogates, etc), instructions must be given
to the students.
3.4 Accuracy
Being aware that instruments may aect the outcome of
experiments.
Being familiar with basic techniques for increasing
experimental accuracy (e.g. measuring many periods instead of a single one, minimizing the influence of noise,
etc).
Knowing that if a functional dependence of a physical quantity is to be determined, the density of taken data
points should correspond to the local characteristic scale
of that functional dependence.
Expressing the final results and experimental uncertainties with a reasonable number of significant digits,
and rounding o correctly.
Data analysis
Transformation of a dependence to a linear form by appropriate choice of variables and fitting a straight line to
experimental points. Finding the linear regression parameters (gradient, intercept and uncertainty estimate)
either graphically, or using the statistical functions of a
calculator (either method acceptable).
Selecting optimal scales for graphs and plotting data
points with error bars.
4 Mathematics
4.1
Algebra
Simplification of formulae by factorisation and expansion. Solving linear systems of equations. Solving equations and systems of equations leading to quadratic and
biquadratic equations; selection of physically meaningful solutions. Summation of arithmetic and geometric
series.
4.2
Functions
4.3
4.4 Vectors
4.7
Calculus