Modern family: Addition

Olympiad preparation (2)

Similar to USAMO, USAPhO exam covers all topics in introductory physics, including mechanics, electromagnetism, thermodynamics, relativity, nuclear, atomic, and particle physics, waves, optics, and data analysis. Problems may require the use of calculus and most of the concepts needed to solve the problems are generally introduced in algebra- based high-school physics courses.

Local level exam for screening generally includes more problems from kinematics, statics, Newton’s laws, momentum and energy, oscillations, orbital mechanics, fluids, and elementary data analysis with few problem from other areas eg. Thermodynamics, nuclear and particle physics etc.

For USAPhO exam specifically, problems focus on testing creativity and understanding of physics rather than testing mathematical virtuosity or speed of working. The proportion of marks allocated for mathematical manipulations are to be kept small. In the case of mathematically challenging tasks, alternative approximate solutions receive partial credit. Problem texts are generally concise; other than the theoretical and the experimental examination is also conducted.

In experimental exam,

1. measurement techniques and apparatus eg. familiarity with the most common experimental techniques for measuring physical quantities mentioned in the theoretical part; knowledge of 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.

2. Experimental uncertainty analysis eg. Identification of dominant error sources, and reasonable estimation of the magnitudes of the experimental uncertainties of direct measurements (using rules from documentation, if provided). Distinguishing between random and systematic errors; being able to estimate and reduce the former via repeated measurements. Finding absolute and relative uncertainties of a quantity determined as a function of measured quantities using any reasonable method (such as linear approximation, addition by modulus or Pythagorean addition).

3. Accuracy eg. Being aware that instruments may affect 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 off correctly.

4. Data analysis eg. 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.

Etc. Etc. are generally accounted for and marks are given based on the performance as per established norms.

Regarding books and materials, I purchased variety of books eg. Physics by Halliday, Resnick and Krane (This is the single- most important book to read to prepare for the USAPhO exam. This book covers everything and contains many challenging problems);

Introduction to Classical mechanics by David Morin (This book will take you deeper into mechanics, including some material (such as Lagrangian mechanics) beyond the syllabus of olympiad);

Electricity and Magnetism by Purcell and Morin (This is a great book on electromagnetism for those who want to learn it with multidimensional and vector calculus);