Slovak Physics Olympiad Cat A: Experimental Physics: Design, Measurement, Errors, Data Treatment

Core concepts

You must be able to design an experiment: identify variables (independent, dependent, controlled), choose instruments with appropriate resolution, and describe a procedure that a reader could repeat. Distinguish random from systematic errors, and precision from accuracy. Report results as value ± uncertainty with consistent significant figures. Combine uncertainties: for sums, add absolute uncertainties; for products/quotients, add fractional uncertainties; for powers, multiply the fractional uncertainty by the exponent. Use repeated measurements and the mean; estimate standard uncertainty. Plot graphs to linearise relations (e.g. T² vs L for a pendulum) and extract parameters from slope and intercept.

Traps

• Reporting too many significant figures.
• Adding fractional and absolute uncertainties inconsistently.
• Ignoring systematic error when it dominates.
• Failing to identify the controlled variables.
• Misreading a graph's slope units.

Worked example

A pendulum: measure L and T for several lengths. Since T = 2π√(L/g), plot T² vs L; slope = 4π²/g, so g = 4π²/slope. Rule of thumb: linearise before fitting - a straight-line slope is far easier to interpret and its uncertainty is easier to estimate.