PHYSICS I P - Z

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 applies 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 unambiguity of language, at different levels and to different, both specialists and non-specialists, audiences.

Learning skills
The ability to learn the scientific concepts of Physics is necessary to undertake subsequent studies with a high degree of autonomy.

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.

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, linear differential equations with constant coefficients.

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.

INTRODUCTORY CONCEPTS

Physical quantities and units. The scientific method. The International System of Units (SI). Scientific notation. Dimensional analysis. Fundamental and derived quantities.

Measurement errors and approximations. Significant figures. Function approximations.

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

MECHANICS

Kinematics. Speed, velocity, acceleration, and time dependence of motion. Uniform and uniformly accelerated rectilinear motion. Vertical motion. Simple harmonic motion. Exponentially damped rectilinear motion. Motion in a plane: velocity and acceleration. Circular motion. Parabolic motion. Motion in three dimensions.

Dynamics of the material point. Newton's laws: inertia, force, and the second and third laws of motion. Impulse and linear momentum. Net force: constraint reactions and conditions of equilibrium. Examples of forces: gravitational force, kinetic friction, viscous friction, centripetal force, elastic force. Inclined plane. Simple pendulum. Tension in strings. Reference frames. Relative velocity and acceleration. Inertial frames. Galilean relativity.

Work and energy. Work, power, and kinetic energy. The work-energy theorem (with proof). Examples of work done by various forces. Conservative and non-conservative forces. Potential energy. Principle of conservation of mechanical energy. Relationship between force and potential energy. Angular momentum. Torque (moment of a force). Central forces.

Dynamics of systems of material points. Systems of particles. Internal and external forces. Center of mass and its properties. Conservation of linear momentum. Conservation of angular momentum. König's theorems (with proofs). Work-energy theorem (with proof). Collisions.

Dynamics of the rigid body. Definition and properties of a rigid body. Motion of a rigid body. Continuous bodies: density and center of mass. Rotational motion about a fixed axis in an inertial frame. Rotational kinetic energy and work. Moment of inertia. Huygens–Steiner theorem (parallel axis theorem, with proof). Compound pendulum. Pure rolling motion. Energy conservation in rigid body motion. Rolling friction.

Oscillations and waves. Properties of the differential equation for harmonic oscillators. Simple harmonic oscillator: equation of motion and solution. Mass-spring systems. Energy of the harmonic oscillator. Damped and driven oscillators. Resonance phenomena.

Gravitation. Kepler's laws. Kepler's laws. Newton's law of universal gravitation. Inertial and gravitational mass. Gravitational field and potential energy.

THERMODYNAMICS

First Principle of Thermodynamics. Thermodynamic systems and states. Thermal equilibrium and the Zeroth Law of Thermodynamics. Temperature and thermometers. Equivalence of heat and work: Joule's experiments. Internal energy. Thermodynamic processes. Work and heat. Calorimetry. Phase transitions. Heat transfer.

Ideal gases. Ideal gas laws. Equation of state for ideal gases. Thermodynamic transformations of a gas. Work and heat in gas processes. Specific heat and internal energy of ideal gases. Analytical study of various transformations. Cyclic processes. The Carnot cycle. Kinetic theory of gases. Equipartition of energy.

Second Principle of Thermodynamics. Statements of the Second Law (with proof of their equivalence). Reversibility and irreversibility. Carnot’s theorem (with proof). Absolute thermodynamic temperature. Clausius theorem (with proof). Entropy as a state function. The principle of increasing entropy in the universe. Entropy change calculations. Entropy of an ideal gas. Unavailable energy.

1. Mazzoldi, Nigro, Voci – Elementi di Fisica - Meccanica e Termodinamica - EdiSES - Terza Edizione
2. Mazzoldi, Nigro, Voci, Fisica – Volume I - EdiSES - Seconda Edizione

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 of 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 of 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 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.

FINAL EXAM

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

The preliminary test consists of 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 Second and Third exam sessions for current students, the student is free to split this test into the following two intermediate tests:

• 1a intermediate preliminary test, which consists of the resolution, justified and clearly commented, of 2 problems of Mechanics in the maximum time of 1 hour;
• 2nd 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 min and consists of 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.

Dates of the exams
Check the following web pages:
https://studenti.smartedu.unict.it/
https://www.dieei.unict.it/corsi/l-8-inf/esami
Exam booking through the Smart_Edu platform is mandatory. Non-booked students will not be able to do exams.

Information for students with disabilities and/or SLD

To guarantee equal opportunities and in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and/or dispensatory measures, according to the educational objectives and specific needs.

It is also possible to contact the CInAP (Centro l'Integrazione Attiva e Partecipata - Servizi per le Disabilità e/o DSA) contact-person of the Department, Prof. Antonella Di Stefano.

Examples of asked questions 

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 solving 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"
"Say 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 a 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, or in the MS-Teams channel of to the course.