Academic Year 2020/2021 - 1° Year

FIS/01 - 9 CFU - 2° Semester

The purpose of the course is to provide basic qualitative and quantitative knowledge on the topics of classical mechanics and thermodynamics included in the "Detailed Course Contents" section, as well as the ability to know how to apply the Scientific Method to solving real and concrete problems.

In particular, and with reference to the so-called Dublin Descriptors, the course aims to provide the following knowledge and skills.

**Knowledge and understanding abilities**

Knowledge of the main phenomenological aspects related to classical mechanics and thermodynamics and understanding of their physical implications and their mathematical description, in order to develop an ability to reflect on scientific issues in a way that presents traits of originality.

**Applying knowledge and understanding ability**

Ability to recognize the main physical laws that govern a phenomenon in mechanics and thermodynamics, and to apply them to solve problems and exercises in different fields and at different levels of complexity, and therefore of approximation, with the use of appropriate mathematical tools.

**Ability of making judgements**

Ability to estimate and calculate the order of magnitude of the variables that describe a physical phenomenon (in mechanics and in thermodynamics). Ability to discern the level of importance of a physical law (axiom, conservation principle, universal law, theorem, law in global / integral or local / differential form and its generality, properties of materials, etc.). Ability to be able to evaluate the Physical Model and the corresponding Mathematical Model that best apply to the description of a physical process and therefore to the solution of quantitative problems.

**Communication skills**

Ability to present scientific concepts belonging to physics but also, and more generally, information, ideas, problems and solutions with properties and inambiguity of language, at different levels and to different, both specialists and non-specialists, audiences.

**Learning skills**

Ability to learn the scientific concepts of Physics, necessary to undertake subsequent studies with a high degree of autonomy.

**Prerequisites**

Although no prerequisite is officially imposed, it is extremely useful for the student to have mastery of the subjects of elementary mathematics (algebra, geometry, trigonometry, analytical geometry) and knowledge of those of mathematical analysis (differential and integral calculus). In fact, for the presentation of the physical concepts included in the course content, the following mathematical tools are used: equations and systems of 1st and 2nd degree equations, trigonometric functions and their properties, exponential functions and their properties, logarithmic functions and their properties, equations of loci in the plane and in space, derivatives and integrals of functions of one variable, constant coefficient linear differential equations.

For the self-paced learning, and/or consolidation, of the required preliminary knowledge, the mathematics and basic calculus courses available on e-learning platforms such as, for example, __Federica Web Learning__ and __Coursera for Campus__, to which students of the University have access, may be useful.

**Attendance to lectures**

Although not compulsory, the attendance of the lectures is strongly recommended. It is now acquired experience that some concepts explained in the classroom during the lectures, and analyzed in detail in classroom sessions of Q&A between learners and teacher, may not be immediately understood in the context of an individual autonomous study. Furthermore, on the basis of statistics gathered in the past years, the time required to pass the final exam and the relative mark obtained significantly depend on whether or not students have followed all the lectures.

**Teaching activity **

The teaching activity consists of lectures and exercises (for a total of 9 ECTS, of which 7 of lectures and 2 of exercises), accompanied by tutoring activities^{(*)}. The exercises provide for the resolution, both guided and autonomous, of tasks and exercises. Where possible, innovative teaching and learning strategies are used. During each lesson, moreover, space is left to students for questions, curiosities and comments, in order to maximize teacher-student interaction.

__ N.B.__: in the event that the contingent situation relating to the COVID-19 pandemic requires it, lectures may also take place electronically on the Microsoft Teams platform (see the

^{(*)}If specialist tutors are available for the course during the academic year.

**Didactic material **

Collections of exercises carried out and organized by levels of increasing difficulty, up to the level required to pass the preliminary exam (s), and presentations (if used by the teacher during the lessons) are published in PDF format in the "Documenti" section of the course page on the Studium portal.

The video recordings, __not edited or formatted__, of the lectures held electronically by the teacher (in Italian) during the Academic Year 2019-2020 due to the COVID-19 pandemic will also be made available.

__ N.B.__: the videotaped lessons could contain topics that are no longer part of the program for the current Academic Year, or not contain topics that are part of it, therefore they

**Learning verification**

__Ongoing tests__

There are two non-compulsory ongoing tests of 1 hour each, the first scheduled during the teaching break of the second semester and the second after the end of the course. __Only current students can take the ongoing tests__.

The first ongoing test consists in solving 2 problems in Mechanics, relating to the topics of the course explained __before__ the teaching break of the second semester. The second ongoing test consists in solving 1 problem in Mechanics, relating to the topics of the course explained __after__ the teaching break of the second semester, and 1 problem in Thermodynamics.

The resolution of each problem is assigned a score between 0/30 and 7.5/30 in relation (1) to the completeness of the description of the Physical and Mathematical Models used for the solution, (2) to the correctness of the mathematical treatment and, of course, (3) to the correctness of the result, both from a numerical and a dimensional point of view.

If the overall score obtained in the two ongoing tests is equal to or greater than 18/30, it is possible to take the oral test directly in one of the sessions of the Second and Third exam sessions for current students. If, on the other hand, the overall score achieved in the two ongoing tests is less than 18/30, it is not recommended to take the oral test. However, being discouraged is __ not__ equivalent to a formal ban on taking the oral exam. However, this must be taken in one of the sessions of the Second and Third exam sessions for current students.

__ N.B.__: in the event that the contingent situation relating to the COVID-19 pandemic requires it, the ongoing tests will be carried out electronically on the Microsoft Teams platform (see the student guide - only in Italian - prepared by the University). The tests will technically take place in the following way:

- A few days before the day set for the test, the booked students will be informed usually by a message on Studium and/or Smart_Edu about the Team code/link that will be used to manage the test.
- On the day and time set for the test, the students who have been booked must access the Team.
- The roll call will then be made and, one by one, those present will have to turn on the camera and the microphone, say their name and surname and show a valid ID in front of the camera.
- After that, the test text will be distributed as a "timed" Activity on Teams.
- From that moment, the students will have 1 hour to carry out the ongoing test and 15 minutes to scan/photograph the pages of the test and upload them to Teams.
.**During the entire time of the test, cameras and microphones must remain on**

__Final exam__

**The final exam consists of a preliminary test followed by an oral exam.**

The __preliminary test consists in the resolution, justified, and clearly commented, of 2 Mechanics problems and 2 Thermodynamics problems in a maximum time of 2 hours__.

__ Only__ in the calls of the Second and Third exam sessions for current students, the student is free to split this test into the following two intermediate tests:

- 1
^{st}intermediate preliminary test, which consists of the resolution, justified and clearly commented, of 2 problems of Mechanics in the maximum time of 1 hour; - 2
^{nd}intermediate preliminary test, which consists of the resolution, justified and clearly commented, of 2 thermodynamic problems in the maximum time of 1 hour.

At the beginning of the preliminary test, the student must inform the teacher if he/she intends to make use of this "exam splitting possibility".

The resolution of each problem will be assigned a score between 0/30 and 7.5/30 in relation (1) to the completeness of the description of the Physical and Mathematical Models used for the solution, (2) to the correctness of the mathematical treatment and, of course, (3) to the correctness of the result, both from a numerical and a dimensional point of view.

The students who obtain a score lower than 18/30 in the preliminary test or in the two intermediate preliminary tests are not recommended to take the oral test. However, being discouraged is __ not__ equivalent to a formal ban on taking the oral exam.

The preliminary test must be taken as part of the **same call in which the student intends to take the oral exam**. In the case of the intermediate preliminary tests, only the __second one__ must be taken as part of the same call in which the student intends to take the oral exam and in any case this call must belong to the Second or Third Session of exams for current students.

The oral exam lasts about 30-40 min and consists in the discussion of at least three (3) distinct topics of the course contents, of which the first is chosen by the student. During the oral exam, proof of theorems and important results included in the program may be required.

__ N.B.__: in the event that the contingent situation relating to the COVID-19 pandemic requires it, the final exam will take place electronically on the Microsoft Teams platform (see the

- A few days before the day set for the test, the students who have been booked will be informed usually by a message on Studium and/or Smart_Edu about the Team code/link that will be used to manage the session.
- On the day and time set for the test, the students who have been booked must access the Team.
- The roll call will then be made and, one by one, those present will have to turn on the camera and microphone, say their name and surname and show a valid ID in front of the camera.
- After that, the text of the preliminary test will be distributed as a "timed" Activity on Teams.
- From that moment, the students will have 1 hour for the intermediate tests and 2 hours for the complete test and 15 minutes for the scanning/photography of their test and subsequent uploading to Teams.
.**During the entire time of the test, cameras and microphones must remain on**

The oral exam will take place technically in the following way:

- A few days before the day set for the oral exam session, the students who have booked will be informed usually by a message on Studium and/or Smart_Edu about the Team code/link that will be used to manage the session.
- On the day and time set for the oral exam session, the students who intend to take the test will have to access the Team.
- The students present will be examined, one by one, and at the beginning of the oral exam they will have to turn on the camera and microphone, say their name and surname show a valid ID in front of the camera.
- During the oral exam, the cameras and microphones of all the other students present must remain off.
- At the end of each oral exam, the final evaluation of the exam will be communicated.

During the oral exam, the camera must be positioned so that it can also frame the sheets which the student can use to complement/justify what he or she says. Alternatively, the student can use other digital "freehand" writing devices (tablets, graphics tablets, touch and/or interactive displays, etc.) whose screen can be shared through Teams.

**Dates of the exams **

Check the following web pages:

Exam booking through the Smart_Edu platform is __ mandatory__. Non-booked students will not be able to do exams.

**Examples of asked questions and exercises**** **

Usually, the oral exam begins with the presentation of a topic chosen by the candidate. The questions asked during the oral exam will be related to the topics of the program. For example:

- "State and demonstrate the principle of conservation of mechanical energy"
- "Show that a central force is conservative"
- "Present and discuss Newton's laws of dynamics"
- "Show how Newton's second law of dynamics allows to solve the general problem of mechanics"
- "State and demonstrate the principle of conservation of momentum"
- "Tell me about the dynamics of a rigid body: degrees of freedom, equations of motion, conservation laws"
- "Tell me about thermodynamic equilibrium and the principle of thermal equilibrium"
- "Recite the statements of the second law of thermodynamics and prove their equivalence"
- "Evaluate the internal energy of an ideal monoatomic gas and an ideal diatomic gas"
- "State and demonstrate Mayer's relationship"
- "State and demonstrate the principle of the increasing entropy of the universe"
- "Say what is meant by unusable energy and calculate it for a transformation of your choice"
- "Say what is meant by thermodynamic function of state"
- etc.

During the oral exam it may be necessary to demonstrate theorems and important results included in the program with numerical evaluations of the order of magnitude of the physical quantities involved in a given phenomenon.

A collection of exercises, many of which were assigned during the preliminary exams, is available in the "Documenti" section of the course page on the Studium portal.

**Course structure**** **

- Physical quantities and units of measure (4 hours) - Reference textbook 1 - Appendix B
- Scalars and vectors (5 hours) - Reference textbook 1 - Appendix C
- Kinematics (9 hours) - Reference textbook 1 - Chapter 1; Reference textbook 2 - Chapter 8
- Dynamics of the material point (12 hours) - Reference textbook 1 - Chapters 2 and 3; Reference textbook 2 - Chapters 9 and 12
- Work and energy (6 hours) - Reference textbook 1 - Chapter 2; Reference textbook 2 - Chapters 4, 10, 13 and 14
- Dynamics of systems of material points (5 hours) - Reference textbook 1 - Chapter 4; Reference textbook 2 - Chapter 19
- Gravitation (4 hours) - Reference textbook 1 - Chapter 5; Reference textbook 2 - Chapter 7
- Dynamics of the rigid body (6 hours) - Reference textbook 1 - Chapter 6; Reference textbook 2 - Chapter 20
- Oscillations and waves (6 hours) - Reference textbook 1 - Chapter 9; Reference textbook 2 - Chapters 21 and 23
- First Principle of Thermodynamics (8 hours) - Reference textbook 1 - Chapter 10; Reference textbook 2 - Chapter 44
- Ideal gases (6 hours) - - Reference textbook 1 - Chapter 11; Reference textbook 2 - Chapter 39
- Second Principle of Thermodynamics (8 hours) - Reference textbook 1 - Chapter 12; Reference textbook 2 - Chapters 45 and 46

**INTRODUCTORY CONCEPTS**

**Physical quantities and units**. The scientific method. Physical quantities and units. The International System (SI). Scientific notation. Dimensional issues. Fundamental and derived physical quantities. Measurement errors and approximations. Significant figures. Functions' approximations..

**Scalars and vectors**. Scalar and vector quantities. Invariance and symmetry. Vector algebra. Vector calculus: derivatives and integrals of vectors.

**MECHANICS**

**Kinematics.** Speed, velocity, acceleration and time dependence of motion. Straight and uniformly accelerated rectilinear motion. Vertical motion. Simple harmonic motion. Rectilinear motion exponentially damped. Motion in a plane: velocity and acceleration. Circular motion. Parabolic motion. Motions in space.

**Dynamics of the material point.** Principle of inertia and the concept of force. Second and third Newton's law. mpulse and momentum. Resulting force: binding reactions and equilibrium. Examples of forces: weight force, sliding friction force, viscous friction force, centripetal force, elastic force. Inclined pkane. Simple pendulum. Wire tension. Reference systems. Relative speed and acceleration. Inertial reference systems. Relativity of Galilei.

**Work and energy**. Work, power and kinetic energy. The theorem of the kinetic energy. Examples of works done by forces. Conservative forces and potential energy. Non-conservative forces. Principle of conservation of mechanical energy. Relationship between force and potential energy. Angular momentum. Torque. Central forces.

**Dynamics of systems of material points.** Systems of points. Internal and external forces. Center of mass and its properties. Principle of conservation of the momentum. Principle of conservation of the angular momentum. The König theorems. Theorem of the kinetic energy. Collisions.

**Dynamics of the rigid body.** Definition of rigid body and its properties. Motion of a rigid body. Continuous bodies, density and the position of the center of mass. Rigid rotations around an axis in an inertial reference system. Rotational energy and work. Moment of inertia. Huygens-Steiner's theorem. Compound pendulum. Pure rolling motion. Energy conservation in the motion of a rigid body. Rolling friction.

**Oscillations and waves.** Properties of the differntial equation of the harmonic oscillator. Simple harmonic oscillator: motion equation and its solution. Motion of a mass connected to a spring. Energy of a simple harmonic oscillator. Damped and forced harmonic oscillators. Resonance.

**Gravitation**. Kepler's laws. The Universal Gravitation Law. Inertial mass and gravitational mass. Gravitational field and gravitational potential energy.

**THERMODYNAMICS**

**First Principle of Thermodynamics**. Thermodynamic systems and states. Thermodynamic equilibrium and the Principle of Thermal Equilibrium. Temperature and thermometers. Equivalence of work and heat: Joule's experiments. First Principle of Thermodynamics. Internal energy. Thermodynamic transformations. Work and heat. Calorimetry. Phase transitions. Heat transmission.

**Ideal gases.** Laws of the ideal gas. Equation of state of the ideal gas. Transformations of a gas. Work. Specific heat and internal energy of the ideal gas. Analytical study of some transformations. Ciclic transformations. The Carnot cycle. Kinetic theory of gases.Equipartition of energy.

**Second Principle of Thermodynamics.** Statements of the Second Principle of Thermodynamics. Reversibility and irreversibility. Carnot's theorem. Absolute thermodynamic temperature. Clausius theorem. Entropy state function. The principle of increasing entropy of the universe. Entropy variations' calculations. Entropy of the ideal gas. Unusable energy.

1. P. Mazzoldi, M. Nigro e C. Voci, *Fisica – Volume I - Seconda **Edizione* (EdiSES, Napoli, 2003);

2. R. P. Feynman, R. B. Leighton e M. Sands, *La Fisica di Feynman – Vol. 1, Parte 1 e Parte 2 *(Zanichelli, Bologna, 2007) - for additional reading - this book is also in English.