Academic Year 2023/2024 - Teacher: SILVIO CHERUBINI

Expected Learning Outcomes

The course gives the background of Laboratory of Physics and Statistics.

The students teach the experimental method and the experimental data analysis techniques. 

The number of hours the student attends the laboratory  is 90 hours. During the experimental work the students are followed by the teacher and a tutor. There is, also,  the  presence of the lab technician.

At the end of the course the student will have:

  • Ability of inductive and deductive reasoning
  • Ability to assemble and fine-tune some basic experimental configurations, and to use scientific instruments for thermomechanical measurements
  • Ability to perform a statistical analysis of experimental data.

Furthermore, in reference to  Dublin Descriptors, this course helps to acquire the following transversal skills:

Knowledge and understanding:

  • Ability of inductive and deductive reasoning.
  • Ability to describe a physical phenomenon in terms of scalar and vector fields.
  • Ability to describe a problem in terms of suitable (algebraic, integral, or differential) relations among physical magnitudes through analytical or numerical methods
  • Ability to assemble and fine-tune some basic experimental configurations, and to use scientific instruments for thermomechanical measurements
  • Ability to perform a statistical analysis of experimental data

Applying knowledge and understanding

  • Ability to apply one's knowledge to describe physical phenomena using scientific methods rigorously.
  • Ability to plan or devise simple experiments and to perform a statistical analysis of the experimental data thereby obtained in all areas of interest of physics, including those with technological applications.

Making judgements

  • Ability of critical reasoning
  • Ability to select the most suitable methods to critically analyze, interpret, and describe experimental data.
  • Ability to identify the predictions of a theory or of a model.
  • Ability to estimate the accuracy of measurements, the linear character of an instrument's feedback, sensitivity and selectivity of the techniques under use.

Communication skills

  • Ability to orally present scientific topics, with a suitable vocabulary and sufficient rigour, with attention to motivations and results.
  • Ability to present scientific topics, in a written form, with a suitable vocabulary and sufficient rigour, with attention to motivations and results.

Course Structure

The teaching is divided into lectures, that will be held in the first part of the course, and experiments to do in the laboratory in the second part.
The frontal hours are dedicated to the measurement method, data analysis and statistical elements. Are provided exercises during head-hours in order to prepare students to perform correctly laboratory experiences that they will do in the second part of the teaching.
6 credits (corresponding to 7 hours each) are dedicated to lessons in the classroom, for a total of 42 hours, and 6 ECTS (corresponding to 15 hours each) are dedicated to laboratory exercises, for a total of 90 hours. The course, of 12 CFU, thus includes a total of 132 hours of teaching activities.

During the course, guided tours will be scheduled to the National Laboratories of the South and to the Research Institutes working at the Department of Physics and Astronomy.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Required Prerequisites

Basic knowledge of Mathematics (elements of analysis) and Physics 1.
It is useful, and therefore strongly recommended, to have passed the exams or to have studied Physics 1 and Mathematical Analysis

Attendance of Lessons

Attendance in the laboratory is mandatory.

Attendance to lectures is usually compulsory.

Attendance signatures are collected during the workshop.

The unjustified absence of more than 25% of laboratory exercises will exclude the student from the possibility of taking the exam in that academic year.
Classroom lessons are normally held 3 times a week, 2 hours each lesson.
The sessions in the Laboratory are normally held 3 times a week, 2 hours each session.

Detailed Course Content

The course is 12 CFU. 132 hours including classroom lessons and laboratory exercises.

In particular, 42 hours of classroom instruction and 90 hours of guided laboratory exercises are planned include both the description of the different experiments in the laboratory and the taking and analysis of the data 

Analysis of the experimental data and statistics

  • The Scientific Method
  • The measurement of physical quantities. Definition (operational) of physical quantities and its measurement. Fundamental and derived quantities. Units of measurement and units of measurement systems: The International System.
  • Presentation of the measures and significant digits. Read a formula and verify its correctness (dimensional analysis)
  • Features of a measuring instrument
  • Errors and / or uncertainties. Systematic and random errors.
  • The total error in measurements, relative error, degree of precision.
  • Measures single and / or multiple. The best estimate of the error (mode, median and mean)
  • Random events, aleatorie- variables classical definition, relative frequency and axiomatic probability - Total probability, conditional probability, likely composed
  • Statistical population - sampling - law of large numbers - mathematical expectation for discrete and continuous random variables - probability density - moments - central limit theorem
  • Standard deviation, population standard deviation, and sample average.
  •  Error propagation.
  •  Representation of data: tables, diagrams and graphs.
  • Histograms: discreetly to limit distribution.
  • The distribution of Gaussian distribution as a limit for measures affected by random errors.
  • The measure of a physical quantity influenced by random events and estimate of the expected value.
  • The criterion of maximum likelihood.
  •  Probability distributions: t-student, Gaussian, Binomial , Poisson and χ2-distribution distribution
  • Test of chi-square.
  • Graphic and functional relationships

Laboratory hours (24 hours in the classroom and in the laboratory) dedicated to:

  • description of measuring instruments: vernier, various types of calipers;
  • description of the mechanical devices used to create and maintain the vacuum;
  • Notes on information technology and computer hardware;
  • Description of laboratory experiences.

Laboratory experiments  (66 hours ):

• Inclined plane •  Fletcher and Atwood Machine Device • Simple pendulum • Physic Pendulum• Kater reversible pendulum • Pendulum ball, spherometer • Pendulum on bow • Torsion Pendulum • Maxwell's • Springs • Moment of inertia of a flywheel • Rotational kinetic energy.

Pycnometer • Mohr-Westphal balance •  Ostwald viscometer• Tension • Venturi tube • Sedimentation, Calorimeter mixtures of Regnault • Heat propagation in a homogeneous beam • -Equazione perfect gas state of Desormes • Experience and Clement • Kundt Tube • Galton Box

Learning assessment may also be carried out on line, should the conditions require this.

Textbook Information

SUGGESTED TEXTS for laboratory, data analysis and statistics

  1. J.R. Taylor: Introduzione all'analisi degli errori. Lo studio delle incertezze nelle misure fisiche,  Zanichelli
  2. M. Loreti: Teoria degli Errori e Fondamenti di Statistica, Decibel, Padova
  3. R. Bevington: Data Reduction and Error Analysis for the Physical Sciences
  4. R. Ricamo: Guida alle Esperimentazioni di Fisica, Ed. Ambrosiana, Milano
  5. E. Perucca: Fisica Generale e Sperimentale, UTET, Torino
  6. F.Tyler: A Laboratory Manual of Physics E.Arnould, London
  7. lecture slides

Course Planning

 SubjectsText References
1See the syllabus for frontal teaching

Learning Assessment

Learning Assessment Procedures

Students from January to June will perform (in groups of 3 or 4 people) the data collection and analysis of some experiences in the laboratory assisted by the teacher.

Each group will be involved in 6 laboratory experiences according to a calendar that will be made available by December.

Each group can choose an experience (As) from table A and an experience (Bs) from table B, taking care to make different choices from those of the other groups. In the event that no agreement is reached, the teacher will settle the disputes.

The remaining four experiences (A1, A2, A3, A4) will be assigned by the teacher, taking them from table A

Each group will have time to acquire the data relating to the chosen experience As by the end of the first teaching period (end of January). Immediately after the end of the first didactic period (mid February) he will have to deliver a report (unique for the group) on said experience As.

This report will constitute the ongoing test.

These reports will be corrected and discussed with the students in the classroom at the resumption of the lessons of the second teaching period; students will receive all the information and suggestions requested also in the data acquisition and processing phase.

During the second teaching period, students will be engaged on the other five experiences, according to the calendar that will be provided to them. In this phase, the teacher's instructions will only concern general issues; each group will have to work independently, taking advantage of what they have already learned from the first experience. In addition, all students will have to take the data from the Galton experiment and process them. The results will be discussed in the classroom.

The student on the exam will take an individual laboratory practical test on an experience drawn from among the four (A1, A2, A3, A4), assigned by the teacher to her group. On this experience you will deliver a report with a complete data analysis, which will be discussed during the oral exam.

Oral exam: it focuses on all the topics of the course and on the experiences explained by the teacher during the course, even if no experiments have been made on these. There will be a broad and detailed discussion on the report presented.

Table A

  • Inclined plane
  • Fletcher Setup
  • Atwood's machine
  • Pendulum (small oscillations)
  • Pendulum (big obcillations)
  • Physical pendulum
  • Spherical pendulum and pendulum on arch
  • Torsion pendulum
  • Maxwell's needle
  • Oscillation of a spring
  • Momento of inertia of a flywheel
  • Kinetic energy of rotation

Table B

  • Kater reversible pendulum
  • Regnault's calorimeter
  • Heat propagation in a homogeneous bar
  • Pycnometer
  • Mohr-Westphal balance
  • Sedimentation
  • Ostwald viscosimeter
  • Surface tension
  • Venturi tube
  • Verification of gas laws
  • Clement-Desormes experiment
  • Kundt tube

If the teaching is given in a mixed or remote mode, the necessary changes with respect to what was previously stated may be introduced, in order to comply with the program envisaged and reported in the syllabus.


As a rule, 7 exam sessions are fixed in each Academic Year; consult the Exam Calendar for the Bachelor's Degree Course in Physics:

As illustrated above, these dates refer exclusively to the practical test. Considering the preparation of the laboratory report and the correction by the teacher, the oral exam will be done about 15/20 days after the practical test.

Verification of learning can also be carried out electronically, should the conditions require it.

Examples of frequently asked questions and / or exercises

Questions below are not an exhaustive list but are just a few examples.

Covariate matrix, propagation of errors in indirect measurements, Chi-square test, questions on the laboratory paper presented.

NB: this list does not in any way mean that these will be all or only some of the questions that will be proposed to students during the oral exam.