Physics

Activity type

Sperimentale e applicativo

SSD

FIS/01

Year

N/D

Semester

N/D

CFU

9

Hours distribution

24 classroom hours, 36 training hours, 36 laboratory hours

Lecturers

Activity type

Sperimentale e applicativo

SSD

FIS/01

Year

N/D

Semester

N/D

CFU

3

Hours distribution

24 classroom hours

Lecturers

LEONETTA BALDASSARRE
LEONETTA BALDASSARRE

GENERAL OBJECTIVES:
The course is aimed at teaching the bases of the experimental method and techniques of statistical analysis of experimental data. For this purpose the course is divided into classroom lessons and laboratory experiences on mechanics. At the end of the course the students will have to: know the meaning and understand the importance of the measure of a physical quantity and its uncertainty; be able to perform simple measurements of physical quantities and to present their results also in graphic form; be able to develop simple programs for analyzing data; know the concept of probability and the basic elements of statistics; know the properties of the main probability distribution functions; perform inference on physics observables; being able to formulate hypotheses and test their reliability based on experimental observations.

Some fundamental mechanics measurements and the principle of operation of basic instruments are discussed from both theoretical and experimental point of view. Many of the experiments carried out also have an educational value since they can be proposed also in the context of secondary school teaching activities.

During the course the student will develop the following skills: collection, analysis, interpretation and presentation of results and data; learning of experimental methods and techniques also having an educational value; developing of algorithms for data analysis and data acquisition using modern computing tools. Moreover, in a more general context the student will increase some of his personal skills, including: the ability to face problems, to work in groups and to follow a protocol; the management of available resources (including time) and safety in a laboratory; the development of communication skills aimed at clear and convincing presentation of the results obtained.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of statistical data analysis
OF 2) Implementation of data analysis algorithms using computing tools
OF 3) Understanding the meaning of a measure
B - Application skills
OF 4) Make measurements of physical quantities and design an experiment
OF 5) Perform probabilistic inference from experimental observations
OF 6) Interpret graphs, tables, and results of a measurement.
OF 7) Formulate hypotheses and compare with experimental observations
C - Autonomy of judgment
OF 8) Judging the reliability and quality of a measurement
D - Communication skills
OF 9) Know how to communicate in written reports the results the experimental work
OF 10) Know how to choose the most appropriate representation of experimental data
E - Ability to learn
OF 11) Use different measuring instruments for mechanical measurements
OF 12) Use your physics and laboratory knowledge creatively

At the end of the course, students will be able to:

1. Analyse the characteristics of an instrument to determine its resolution.
2. Apply statistical methods to establish whether and to what extent two physical quantities are correlated.
3. Assess the compatibility between two experimental measurements.
4. Calculate and estimate the uncertainty associated with a derived physical quantity.
5. Correctly communicate the result of a measurement, respecting scientific conventions.
6. Determine and evaluate the uncertainty of a direct or indirect measurement.
7. Apply the least squares method to perform a linear fit and judge its robustness.
8. Perform and interpret a Chi-square test to analyse the quality of a fit.
9. Describe the main characteristics of uniform, binomial, Poisson, Gaussian and standard normal probability distributions.
10. Compare different probability distributions to recognise similarities, differences and areas of application.
11. Apply probability distributions in simple experimental or simulation contexts.

In order to successfully complete the course, it is essential to:

1. have a basic knowledge of mathematical analysis, in particular the ability to calculate derivatives and integrals;
2. be able to write simple programmes in any programming language.

It is also useful to be familiar with the basics of the Python language (basic structures, variable management, elementary functions).

It is advisable to review the main concepts of algebra and elementary functions in order to facilitate understanding of the quantitative methods covered in the course.

Module: LABORATORY OF MECHANICS I
N/D
Module: LABORATORY OF MECHANICS II
A) Physical quantities:
- Measurement of a physical quantity: direct measures and indirect measures;
- Fundamental quantities and derived quantities.
- Dimensions of a physical quantity; units of measurement systems.
- random uncertainties and systematic errors;
- Study of the dependance of a quantity according to another;
- plots and their use; frequency histograms.
- Design of simple mechanics experiments

B) Statistical analysis of experimental data with exercises in the classroom
- Definitions of probability. Conditional probability. Composite probability theorems and total probability.
Discrete random variables and probability distribution. Continuous random variables and probability density.
Parameters of a probability distribution function: expected value and variance.
- Some probability distribution functions: Bernoulli distribution, Poisson distribution,
uniform distribution, distribution of Gauss.
- Functions of multiple random variables and covariance matrix.
- The central limit theorem. Law of large numbers.
- Measurement of a physical quantity as a random variable; definition of measurement uncertainty through variance.
- Propagation of uncertainties in indirect measures.
- Statistical inference. Estimation of the parameters of a probability distribution function
starting from a sample of the population; the arithmetic mean, the standard deviation and their properties.
- Estimation of the parameters of a linear relation.
- Comparison between observed and predicted frequency distributions.
- Hypothesis testing. the Chi2 method.

The laboratory activity includes experiments of classical mechanics including: the study of motion of a body subjected to an elastic force, the study of the motion of a body on a sloping plane, the measurement of the gravity acceleration with a simple pendulum, counting measurements (Geiger counter); the study of the motion of a rotating body around a fixed axis (flywheel), the torsion pendulum, the fluids.

Module: LABORATORY OF MECHANICS I
N/D
Module: LABORATORY OF MECHANICS II
Dispense del corso messe a disposizione degli studenti.

C.Bini "Lezioni di Statistica per la Fisica Sperimentale", Nuova Cultura Editrice.

J.R. Taylor “Introduzione all’analisi statistica degli errori”, Zanichelli

P. Fornasini “The Uncertainty in Physical Measurements: An Introduction to Data Analysis in the Physics Laboratory”, Springer

Module: LABORATORY OF MECHANICS I
N/D
Module: LABORATORY OF MECHANICS II
N/D

Lectures are held in the classroom (48 hours). Students are required to participate actively, stimulated by direct questions, discussions and real-time surveys. Contributions may be requested either individually or in groups, in order to encourage involvement and progressive understanding of the concepts.

Classroom exercises (36 hours) aim to consolidate the knowledge acquired and develop practical skills through guided problem solving and the use of IT tools for data analysis.

Laboratory activities (36 hours) are carried out in groups, under the supervision of the lecturer and his/her assistants. Students are given considerable autonomy in defining the methods and tools used to achieve results, in order to stimulate critical thinking, collaboration skills and responsibility in experimental work.

Attendance at laboratory activities is compulsory. Only one absence is permitted, exclusively for justified reasons.

In order to be admitted to the final examination, it is essential to have completed both individual laboratory exercises.

If circumstances require, it is possible to carry out remedial work, aimed at ensuring that the minimum requirements for admission to the oral examination are met, in agreement with the lecturers of the other channels.

The assessment aims to ascertain the effective achievement of the expected learning outcomes, in line with the course's educational objectives. To ensure transparency and awareness, students are provided with a self-assessment grid before each written exam.

The overall assessment is not based on a simple sum of the marks obtained in the individual tests, but takes into account progress, aptitude and active participation during the course. Ongoing tests are given increasing weight.

Structure of the tests:

1. Written test on basic statistics
Type: written test with numerical answer exercises and open-ended questions.
Objective: to test knowledge of probability distributions and the ability to apply them to simple experimental contexts.
Indicative weighting in the final assessment: 10%.
Timing: at the end of the course.

2. Ongoing group tests in the laboratory

Type: laboratory
Objective: to assess the ability to apply the methods learned to the analysis of real and simulated data.
Method: practical, with use of computers and final written report.
Approximate weighting: 20%.
Timing: distributed throughout the course, with increasing weighting.

3. Practical laboratory tests

Type: laboratory report and assessment of experimental skills.
Objective: to verify the individual's ability to collect, process and present experimental data, estimating uncertainties and assessing the compatibility between measurements.
Method: continuous assessment of laboratory activities and written reports.
Approximate weighting: 20%.
Timing: the first after the first three exercises, the second at the end of the course.

4. Final oral exam

Type: individual interview.
Objective: to assess overall mastery of concepts, critical ability to interpret experimental results, use of scientific language and connection between theoretical, practical and computational aspects.
Approximate weighting: 50%.

Timing: at the end of the course.

Bayes' theorem
Kolmogorov axioms
Mean and variance
Moments of a distribution
Propagation of uncertainties
Uncertainty of the mean
Uniform distribution
Binomial distribution
Poisson distribution
Gaussian distribution
Normal Distribution
Maximum Likelihood Principle
Chi-square Test
Least Squares Method
Chebyshev's Inequality
Markov's Inequality

Module: LABORATORY OF MECHANICS I
N/D
Module: LABORATORY OF MECHANICS II
N/D