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, 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 relating 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 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.
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 various levels and to different, both specialists and non-specialists, audiences.
Ability to learn the scientific concepts of Physics, necessary to undertake subsequent studies with a high degree of autonomy.
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.
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.
(*) If specialist tutors are available for the course during the academic year.
NB: 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 student guide - only in Italian - prepared by the University). In that case, appropriate modifications to what is stated in this document may be introduced, in order to achieve the main objectives of the course and the curriculum, described in the "Learning Objectives" and "Detailed Course Content" sections.
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 do not replace the presence in the classroom and the study of textbooks).
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.
NB 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:
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 sessions of the Second and Third exam sessions for current students, the student is free to split this test into the following two intermediate tests:
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.
NB 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 student guide prepared by the University).
The preliminary test and/or the intermediate preliminary tests will technically take place in the following way:
The oral exam will take place technically in the following way:
Dates of the exams
Check the following web pages:
Please note that exam booking is MANDATORY and has to be done online through the Smart_Edu platform. Students without a regular exam booked cannot take 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"
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.
1. Physical quantities and units of measure (4 hours) - Appendix B of the textbook 1
2. Scalars and vectors (5 hours) - Appendix C of the textbook 1
3. Kinematics (9 hours) - Chapters 1 and 2 of the textbook 1
4. Dynamics of the material point (12 hours) - Chapters 3 and 5 of the textbook 1
5. Work and energy (6 hours) - Chapter 4 of the textbook 1
6. Dynamics of systems of material points (5 hours) - Chapters 6 and 8 of the textbook 1
7. Gravitation (4 hours) - Chapter 11 of the textbook 1
8. Dynamics of the rigid body (6 hours) - Chapter 7 of the textbook 1
9. Oscillations and waves (6 hours) - Chapter 10 of the textbook 1
10. First Principle of Thermodynamics (8 hours) - Chapter 12 of the textbook 1
11. Ideal gases (6 hours) - Chapter 13 of the textbook 1
12. Second Principle of Thermodynamics (8 hours) - Chapter 14 of the textbook 1
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.
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. Impulse 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.
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.