# PHYSICS I P - Z

**Academic Year 2024/2025**- Teacher:

**FRANCESCO MARIA DIMITRI PELLEGRINO**

## Expected Learning Outcomes

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.

## Course Structure

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.*

## Required 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, 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.

## Attendance of Lessons

## Detailed Course Content

**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. 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 plane. Simple pendulum. Wire tension. Reference systems. Relative speed and acceleration. Inertial reference systems. Galilean Relativity.

**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 differential 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. The entropy of the ideal gas. Unusable energy.

## Textbook Information

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

2. Mazzoldi, Nigro, Voci, Fisica – Volume I - EdiSES - Seconda Edizione

## Course Planning

Subjects | Text References | |
---|---|---|

1 | Physical quantities and units of measure (4 hours) | Reference textbook 1 - Appendix B |

2 | Scalars and vectors (5 hours) | Reference textbook 1 - Appendix C |

3 | Kinematics (9 hours) | Reference textbook 1 - Chapter 1-2 |

4 | Dynamics of the material point (12 hours) | Reference textbook 1 - Chapter 3-5 |

5 | Work and energy (6 hours) | Reference textbook 1 - Chapter 4 |

6 | Dynamics of systems of material points (5 hours) | Reference textbook 1 - Chapter 6 |

7 | Gravitation (4 hours) | Reference textbook 1 - Chapter 11 |

8 | Dynamics of the rigid body (6 hours) | Reference textbook 1 - Chapter 7 |

9 | Oscillations and waves (6 hours) | Reference textbook 1 - Chapter 10 |

10 | First Principle of Thermodynamics (8 hours) | Reference textbook 1 - Chapter 12 |

11 | Ideal gases (6 hours) | Reference textbook 1 - Chapter 13 |

12 | Second Principle of Thermodynamics (8 hours) | Reference textbook 1 - Chapter 14 |

## Learning Assessment

### Learning Assessment Procedures

**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 30-40 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:

http://portalestudente.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 frequently asked questions and / or exercises

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.

**VERSIONE IN ITALIANO**