Physical quantities. Dimensional analysis. Systems of units of measure. Scientific notation. Measurement uncertainties and their estimation (type A and B). Significant figures (digits). Direct measurements. Characteristics of measuring instruments. Mean, standard deviation, standard deviation of the mean. Chance. Probability distributions (constant and Gaussian). Standard uncertainty. Propagation of measurement uncertainties. Linear regression. Experiences on prism, lenses, simple pendulum.
1. Giuseppe Ciullo. Introduzione al Laboratorio di Fisica (Cap. 1-6). Springer
2. John R. Taylor. Introduzione all'analisi degli errori (Cap.1-4). Zanichelli
3. G. D'Agostini, F. Bellini, A. Messina. Dispense
Laboratorio di Meccanica. Sapienza – Università di Roma. (2019)
https://drive.google.com/file/d/1ldBV6nmzLCRbhn
rj7OnK8w_Wo8IhWRY6/view
Learning Objectives
Knowledge.
Concept of measurement of a physical quantity and its uncertainty.
Significant digits. Dimensional analysis.
Statistical uncertainties. Mean, standard deviation, standard deviation of the mean.
Systematic uncertainties. Propagation of uncertainty.
Skills.
Know how to assess the correctness of a relation between physical quantities using the dimensional analysis.
Know how to take simple measurements of physical quantities by analogical and digital instruments.
Know how to use measurement equipments of general use like multimeters, current and voltage sources, etc.
Know how to graphically represent experimental data.
Know how to extract trends between measured physical quantities, verifying simple physical laws.
Know how to draw up a laboratory report.
Know how to use a scientific calculator or a computer for data analysis.
Competence.
Conduct simple experiments, assessing the possible uncertainty sources and the reliability of the measurements.
Prerequisites
Required courses: none
Recommended courses: MATEMATICA I, FISICA I
In particular, it is recommended to review the following topics:
1. Percentage. Simple algebraic calculations. First and second degree algebraic equations.
2. Perimeters, aree and volumes of the most common plane and solid figures.
3. Real function of real variable: polynomials, logarithms, exponentials
4. Derivative of functions (review all the most common derivative rules)
5. Conversion between unit of measurements (example: how many cubic centimeters correspond to a liter?)
Teaching Methods
CFU: 6
Total hours of the course: 150 (6x25)
Hours reserved to private study and other individual formative activities: 90
Hours for Lectures: 24
Hours for Lectures in Laboratory: 0
Hours for Laboratory experiments: 36
Seminars (hours): 0
Stages: 0
Intermediate examinations: 0
Type of Assessment
Group reports on the laboratory experiments.
Final written test.
Course program
The scientific method. Basic physical quantities and derived physical quantities. Dimensions and dimensional analysis. Units of measure and systems of units of measure. Scientific notation. Prefixes for multiples and submultiples. Conversion between units of measure.
Measurement errors and uncertainties. Measurement uncertainties and their sources. How to write the result of a measurement. Precision and accuracy. Significant figures (digits). Relative uncertainty and percentage relative uncertainty. How to write a table. How to prepare a graph.
Direct measurements. Characteristics of measuring instruments. Uncertainties of type A and type B. Systematic errors.
Descriptive and inferential statistics. Univariate analysis: mean, standard deviation (of the population and sample) and standard deviation of the mean. Bivariate analysis: Pearson correlation index. Definition of probability through the bet (B. de Finetti). Probability estimation (combinatorics, frequency analysis, subjective probability, ...). Bayes' theorem and its link with the concept of measure. Probability distributions (rectangular and Gaussian). Expected value and variance. Central limit theorem and its link with the concept of measure. Standard uncertainty.
Estimation of measurement uncertainties with statistical methods. Estimation of systematic errors and their correction. Repeatability and reproducibility.
Comparison between measures (consistent or non-consistent measures).
Propagation of measurement uncertainties in the absence of correlations (sum in quadrature with partial derivatives). Formulas for the propagation of uncertainties in some particular cases.
Combination of multiple results.
Linear regression (linear fit) and the least squares method. Goodness of a fit and coefficient of determination.
Experience on the measurement of the refractive index of a prism
Experience in measuring the focal distance of a lens
Experience in measuring the acceleration of gravity using a simple pendulum