Academic Year 2018/2019 - 1° Year

FIS/01 - 9 CFU - 2° Semester

The course aims at providing basic knowlegde of classical mechanics and thermodynamics topics included in the Course Content (see below) as well as the capability to apply the Scientific Method to the resolution of real and concrete problems.

In particular, the course has the objectives to provide pupils with the following knowledge and abilities.

**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.

**Applying knowledge and understanding ability**

Ability to recognize the main physical laws that govern a mechanic or thermodynamic phenomenon, and to apply them to solve problems and exercises at different levels of complexity and therefore of approximation, with the use of appropriate analytical and numerical techniques.

**Ability of making judgements**

Evaluation of the order of magnitude of the variables that describe a mechanic or thermodynamic phenomenon. Evaluation of the relevance of a physical law (axiom, principle of conservation, universal law, theorem, law in global/integral or local/differential form and its generality, properties of materials, etc.).

**Communication skills**

Capability to expose scientific concepts in a proper and inambiguous manner, at various levels.

**Learning skills**

Application to Physics of theoretical/mathematical techniques.

**Prerequisites**

Although no prerequisites are officially imposed, it is extremely useful that students master the subjects of elementary mathematics (algebra, geometry, trigonometry, analytic geometry) and have knowledge of those of differential and integral calculus.

**Attendance to lectures**

Although it is not mandatory, attendance to classroom lectures is strongly recommended.

**Didactic activity **

Didactic activity consists of classroom lectures and exercises. Exercises can be both assignments of the teacher for the homework or driven by the teacher - or by tutors, if available - in the classroom.

**Didactic material **

A collection of exercises, many of which were assigned during the written exam sessions, is available on the web page of the course in the Studium portal (http://studium.unict.it), inside the section called Documenti.

**Learning verification**

The final exam consists of a written test followed by an oral exam. The written test, lasting 2 hours, consists in the resolution, justified and clearly commented, of 2 problems of Mechanics and of 2 problems of Thermodynamics. At the resolution of each problem will be assigned a score between 0/30 and 7.5/30.

Students who obtain a score lower than 15/30 in the written test are advised against taking the oral exam. To be advised against is not equivalent to a formal prohibition to take the oral exam.

The oral exam consists in the discussion of at least 3 different topics, of which the first is chosen by the student.

The students who have passed both "in itinere" tests are admitted directly to the oral exam. During the oral examination 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.

**Dates of the exams **

Check the following web pages

and the notices on the course page on the Studium portal (http://studium.unict.it) for details on the time and place of the exams and any changes

**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 exactly to the topics of the program. For example:

- "enunciate and demonstrate the principle of conservation of mechanic energy"
- "present and discuss the 3 Newton's laws of mechanics"
- "enunciate and demonstrate the principle of momentum conservation"
- "discuss the dymanics of a rigid body: degrees of freedom, equations of motions and conservation laws"
- "tell me about the thermodynamic equilibrium and the principle of thermal equilibrium"
- "say aloud the enunciates of the second principle of thermodinamycs and demonstrate their equivalence"
- "evaluate the internal energy of monoatomic gas and that of a biatomic one"
- 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 written exam sessions, is available on the course page on the Studium portal (http://studium.unict.it), in the Documents section.

**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

**Physical quantities and units**. Physical sizes and units of measurement. The International System (SI). Mechanical and thermodynamic quantities. Dimensional issues. Measurement errors and approximation. Scientific notation.

**Scalars and vectors**. Scalar and vector quantities. Invariance and symmetry. Vector algebra. 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. Motions in the plane: parabolic motion. Circular motion. Motions in space.

**Dynamics of the material point.** Principle of inertia and concept of force. Second and third Newton's law. Examples of forces: weight force, friction force, elastic force, centripetal force. Resulting force: binding reactions and equilibrium. Impulse and momentum. Reference systems. Relative speed and acceleration. Relativity of Galilei.

**Work and energy**. Work, power and kinetic energy. Examples of work 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.

**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.

**Dynamics of the rigid body.** Definition of rigid body and its properties. Motion of a rigid body. Rigid rotations around an axis in an inertial reference system. Rotational energy and work. Moment of inertia. Huygens-Steiner's theorem. Pure rolling motion. Conservation laws in the motion of a rigid body.

**Oscillations and waves.** Simple harmonic oscillator: motion equation and its solution. Motion of a mass connected to a spring. Energy of a simple harmonic oscillator. Sum of harmonic motions in 1 and 2 dimensions. Damped and forced harmonic oscillators. Resonance.

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

**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. Calorimetry. Phase changes. Heat transmission.

**Ideal gases.** Laws of ideal gases. Equation of state of ideal gases. Transformations of a gas. Work. Specific heat and internal energy of an ideal gas. Analytical study of some transformations. Kinetic theory of gases.

**Second Principle of Thermodynamics.** Statements of the Second Principle of Thermodynamics. Reversibility and irreversibility. Carnot's theorem. Absolute thermodynamic temperature. Clausius theorem. Entropy. The principle of increasing entropy. 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.