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.
The workshop notebook, which is the certificate of attendance for the course, must contain the 3 group reports corresponding to the 3 experiences. The notebook is only one per group and will be handed in after all three experiences have been carried out.
Final written test. The final written exam is divided into two parts. The first part is a check on the basic knowledge needed to carry out experimental work in a laboratory. The second part is a check on the other topics covered in the laboratory course. Passing the first part of the exam is a necessary condition for passing the exam.
Two hours are given for the conduct of the exam, and the number of exercises that must be done is 11. The first six exercises are those related to the fundamental knowledge of the course on a grade of at least 83 percent correct answers is required.
Course program
Physical Quantities and Units of Measurement
The scientific method. Basic physical quantities and derived physical quantities. Dimensions and Dimensional Analysis. Units of measurement and systems of units. Scientific Notation. Prefixes for multiples and submultiples. Conversion between units of measurement.
Measurement Uncertainties and Direct Measurements of a Physical Magnitude.
Measurement errors and uncertainties. Measurement uncertainties and their sources. How to write down the result of a measurement. Precision and accuracy. Significant figures. Relative uncertainty and percentage relative uncertainty. How to write a table. How to prepare a graph. Direct measurements. Characteristics of measuring instruments. Type A and type B uncertainties. Random errors. Systematic errors. Estimation of systematic errors and their correction. Repeatability and reproducibility of a measurement. Comparison of measurements (consistent or non-consistent measurements).
Statistics, probability and measurement uncertainties.
Descriptive and inferential statistics. Uni-variate analysis: mean, standard deviation (of population and sample) and standard deviation of the mean. Bi-variate analysis: Pearson's correlation index. Definition of probability by betting (B. de Finetti). Probability estimation (combinatorial calculus, frequency analysis, subjective probability, .). Probability distributions (rectangular and Gaussian). Expected value and variance. Central limit theorem and its connection with the concept of measurement. Standard uncertainty. Estimation of measurement uncertainties by statistical methods.
Indirect Measurements.
Uncertainties in indirect measurements of a physical quantity. Propagation of measurement uncertainties in the absence of correlations (sum in quadrature with partial derivatives). Formulas for propagation of uncertainties in some special cases. Combination of multiple results.
Linear fits
Linear regression (linear fit) and the method of least squares. Goodness of fit and coefficient of determination.
Laboratory Experiences.
Experience on measuring the refractive index of plexiglass using Snell's law.
Experience on measuring the refractive index of a prism.
Experience on measuring the focal distance of a lens.