PHYSICS I A - E

The course aims to provide basic qualitative and quantitative knowledge of the topics in Classical Mechanics and Thermodynamics included in the "Course content" section, as well as the ability to apply the Scientific Method to the solution of 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

Knowledge of the main phenomenological aspects of classical mechanics and thermodynamics and understanding of their physical implications and of their mathematical description, so as to develop an ability to reflect on scientific questions in a way that shows traits of originality.

Applying knowledge and understanding

Ability to recognise the main physical laws governing 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, using appropriate mathematical tools.

Making judgements

Ability to estimate and calculate the order of magnitude of the variables describing 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 degree of generality, properties of materials, etc.). Ability to assess the Physical Model and the corresponding Mathematical Model that best apply to the description of a physical process and hence to the solution of quantitative problems.

Communication skills

Ability to present scientific concepts proper to Physics, but also, and more generally, information, ideas, problems and solutions with correct and unambiguous language, at different levels and to different audiences, both specialist and non-specialist.

Learning skills

Ability to learn the scientific concepts proper to Physics that are necessary to undertake further studies with a high degree of autonomy.

The teaching activity consists of lectures and exercise sessions, for a total of 9 ECTS credits, of which 7 for lectures (49 hours) and 2 for exercise sessions (30 hours), supported by tutoring activities (*). The exercise sessions involve solving problems and exercises, both with guidance and independently. During each class, interaction is encouraged, leaving room for questions, comments and points of interest.

If the course is delivered in blended or remote mode, appropriate adjustments may be made to the above, in order to ensure consistency with the syllabus.

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

Although no formal prerequisite is imposed, it is extremely useful for students to have a good command of elementary mathematics (algebra, geometry, trigonometry, analytical geometry) and a knowledge of calculus (differential and integral).

The following mathematical tools are used in presenting the physical concepts included in the course content: equations and systems of first- and second-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, and linear differential equations with constant coefficients.

Students who wish to acquire or consolidate the required background independently may find useful the basic mathematics and calculus courses available on e-learning platforms such as Federica Web Learning and Coursera for Campus, to which University students have access.

Although not compulsory, attendance at lectures is strongly recommended. Experience has shown that some concepts explained in class, and discussed in detail during question-and-answer sessions with the students, may not be immediately clear when studying independently. Furthermore, on the basis of statistics gathered in past years, the time needed to pass the final examination and the mark obtained are significantly correlated with whether or not students have attended all the lectures.

INTRODUCTORY CONCEPTS

Physical quantities and units. The scientific method. The International System of Units (SI). Scientific notation. Dimensional analysis. Fundamental and derived physical quantities. Measurement errors and approximations. Significant figures. Approximation of functions.

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

MECHANICS

Kinematics. Velocity, acceleration and the equation 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. Projectile motion. Motion in space.

Dynamics of a particle. The principle of inertia and the concept of force. Newton's second and third laws. Impulse and momentum. Resultant of forces: constraint reactions and equilibrium. Examples of forces: weight, sliding friction, viscous friction, centripetal force, elastic force. The inclined plane. The simple pendulum. Tension in strings. Reference frames. Relative velocity and acceleration. Inertial reference frames. Galilean relativity.

Work, energy, angular momentum. Work, power and kinetic energy. The work-energy theorem. Examples of work done by forces. Conservative forces and potential energy. Non-conservative forces. Conservation of mechanical energy. Relationship between force and potential energy. Angular momentum. Torque. Central forces.

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

Oscillations and waves. Properties of the differential equation of the harmonic oscillator. The simple harmonic oscillator: equation of motion and its solution. Motion of a mass attached to a spring. Energy of the simple harmonic oscillator. Damped and forced harmonic oscillators. Resonance.

Dynamics of systems of particles. Systems of particles. Internal and external forces. The centre of mass and its properties. Conservation of momentum. Conservation of angular momentum. König's theorems. The work-energy theorem. Collisions.

Dynamics of the rigid body. Definition of a rigid body and its properties. Motion of a rigid body. Continuous bodies, density and position of the centre of mass. Rigid rotations about an axis in an inertial reference frame. Rotational work and energy. Moment of inertia. The Huygens-Steiner theorem. The compound pendulum. Pure rolling motion. Energy conservation in the motion of a rigid body. Rolling friction.

THERMODYNAMICS

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

Ideal gases. The ideal gas laws. The equation of state of an ideal gas. Transformations of a gas. Work. Specific heat and internal energy of an ideal gas. Analytical study of selected transformations. Cyclic transformations. The Carnot cycle. Kinetic theory of gases. Equipartition of energy.

The Second Law of Thermodynamics. Statements of the Second Law of Thermodynamics. Reversibility and irreversibility. Carnot's theorem. Absolute thermodynamic temperature. Clausius' theorem. Entropy as a state function. The principle of increase of the entropy of the universe. Calculations of entropy changes. Entropy of an ideal gas. Unavailable energy. 

(1) Teaching material and weekly exercises with detailed solutions, made available by the lecturer on the University's online platform, https://elearning.unict.it/, in the dedicated course area.

(2) Mazzoldi P., Nigro M., Voci C., "Fisica I Vol. I - Meccanica e Termodinamica", EdiSES, III Edizione, 2023.

Publisher's website: www.edises.it/universitario/mazzoldi-nigro-voci-fisica-vol-i-meccanica-e-termodinamica-iii-ed-3690.html

The assessment consists of a written examination followed by an oral examination. Two assessment methods are available, as described below.

1. In-itinere written tests + oral examination

Method available only to students within the prescribed duration of their degree programme (studenti in corso).

In-itinere written tests

Two non-compulsory in-itinere written tests are scheduled, each lasting 1 hour: the first during the teaching break of the second semester, the second after the end of the course. Only students within the prescribed duration of their degree programme may sit these tests.

The first test consists of solving 2 problems in Mechanics, relating to the topics covered before the teaching break of the second semester. The second consists of solving 1 problem in Mechanics, relating to the topics covered after the teaching break, and 1 problem in Thermodynamics.

The solution of each problem is awarded a score between 0/30 and 7.5/30, according to (1) the completeness of the description of the physical and mathematical models used, (2) the correctness of the mathematical treatment, and (3) the correctness of the result, both numerically and dimensionally.

If the overall score obtained in the two in-itinere tests is equal to or higher than 18/30, the student may take the oral examination directly in one of the Second or Third session exam dates reserved for students within the prescribed duration of their programme. If the overall score is lower than 18/30, the student is advised against taking the oral examination; this is a recommendation and not a formal prohibition, and the oral examination must in any case be taken in one of the Second or Third session exam dates. 

Oral examination

The oral examination lasts approximately 30 minutes and consists of the discussion of at least three distinct topics of the syllabus, the first of which is chosen by the student.

During the oral examination, the student's ability to explain clearly, confidently and logically the physical meaning and the physical implications of a given phenomenon will be assessed; this includes the use of mathematical equations, with attention to the definition of all the quantities involved, and possibly the offering of insights that go beyond what was covered in class, demonstrating independent reflection and study. The ability to synthesise and to establish connections between the different topics of the syllabus will also be assessed. Finally, familiarity with the mathematical proofs of theorems and important results included in the syllabus will be assessed, together with the ability to provide numerical estimates of the order of magnitude of the physical quantities involved in a given phenomenon.

2. End-of-course preliminary written test + oral examination

Standard method, available to all students.

Preliminary written test

It consists of the solution, clearly justified and commented, of 2 problems in Mechanics and 2 problems in Thermodynamics, within a maximum time of 2 hours.

Only in the Second and Third session exam dates, students within the prescribed duration of their degree programme may, if they so wish, split this test into two intermediate preliminary written tests:

1. the first consists of the solution, clearly justified and commented, of 2 problems in Mechanics, within a maximum time of 1 hour;
   
2. the second consists of the solution, clearly justified and commented, of 2 problems in Thermodynamics, within a maximum time of 1 hour.
   

At the beginning of the preliminary written test, students must inform the lecturer if they intend to make use of this possibility.

The solution of each problem is awarded a score between 0/30 and 7.5/30, according to the same criteria indicated for the in-itinere tests. Students who obtain a score lower than 18/30 in the preliminary test, or overall in the two intermediate preliminary tests, are advised against taking the oral examination; this is a recommendation and not a formal prohibition.

The preliminary written test must be taken within the same examination session in which the student intends to take the oral examination. In the case of the intermediate preliminary tests, only the second must be taken within the same examination session as the oral examination; that session must in any case belong to the Second or Third session of examinations for students within the prescribed duration of their programme. 

Oral examination

The oral examination lasts approximately 30 minutes and consists of the discussion of at least three distinct topics of the syllabus, the first of which is chosen by the student.

During the oral examination, the student's ability to explain clearly, confidently and logically the physical meaning and the physical implications of a given phenomenon will be assessed; this includes the use of mathematical equations, with attention to the definition of all the quantities involved, and possibly the offering of insights that go beyond what was covered in class, demonstrating independent reflection and study. The ability to synthesise and to establish connections between the different topics of the syllabus will also be assessed. Finally, familiarity with the mathematical proofs of theorems and important results included in the syllabus will be assessed, together with the ability to provide numerical estimates of the order of magnitude of the physical quantities involved in a given phenomenon.

Criteria for the final mark

The final mark takes both exams into account: the score obtained in the written test is the starting point, which the assessment of the oral examination may raise or lower. The final mark is expressed out of thirty and is awarded so as to correspond to the following scheme:

• Fail: the student does not possess the minimum required knowledge of the main contents of the course; is unable to set up the solution of a problem in mechanics or thermodynamics or to apply the acquired knowledge autonomously. The ability to use specific terminology is poor or absent.
  
• Mark 18-21: the student has minimal knowledge of the syllabus topics and sets up the solution of problems in a rudimentary way, with inaccuracies in the mathematical treatment or in the dimensional check of the results; has a modest ability to connect the topics of the syllabus with one another and to analyse the situations presented critically; presents the topics in a sufficiently clear manner although command of language is poorly developed.
  
• Mark 22-25: the student has a fair knowledge of the syllabus topics, albeit limited to the main ones, and solves the corresponding problems correctly, giving reasons for the physical model adopted; is able to connect the topics of the syllabus with one another and to analyse the situations presented critically, though not always in a linear way; presents the topics fairly clearly with a fair command of language.
  
• Mark 26-28: the student has a good knowledge of the syllabus topics and solves problems autonomously, justifying the physical and mathematical models used and checking the numerical and dimensional correctness of the result; is able to connect the topics of the syllabus with one another and to analyse the situations presented critically and linearly; presents the topics clearly using appropriate language.
  
• Mark 29-30 cum laude: the student has a thorough knowledge of the syllabus topics and independently tackles problems even of high complexity, discussing the limits of validity of the approximations adopted; readily and correctly connects the topics of the syllabus with one another and critically analyses the phenomena presented; has excellent communication skills and command of language.
  

Exam dates

Please check the following web pages:

https://studenti.smartedu.unict.it/

https://www.dieei.unict.it/corsi/l-8-inf/esami

Booking through the Smart_Edu platform (https://studenti.smartedu.unict.it/) is compulsory. Students who have not booked will not be admitted to the examination.

Information for students with disabilities and/or specific learning disorders (SLD)

To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l'Integrazione Attiva e Partecipata — Servizi per le Disabilità e/o i DSA) referring teacher within their department (https://www.cinap.unict.it/content/referenti), Prof. Antonella Di Stefano.

Additional information

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

Written examination. The mechanics and thermodynamics problems set in both the in-itinere written tests and the end-of-course preliminary written tests are very similar to those proposed in the weekly exercise sessions held throughout the semester. Before each in-itinere written test, one exercise session will be devoted to a mock test carried out in class.

Oral examination. The oral examination consists of a presentation on a topic of the student's choice, followed by two questions on distinct topics taken from the syllabus (see the "Course content" section for a detailed list of topics).