## Learning objectives

At the end of the course, the student is expected to be able to:

[Knowledge and understanding]

- know the fundamental laws of classical Mechanics, including systems dynamics, and of Thermodynamics, with particular focus on kinematics, Newton’s laws and conservation principles;

- know the main aspects of the dynamics of rigid bodies, gravitation, oscillatory and wave phenomena and of the Theory of Special Relativity;

- explain the origin of the depicted phenomena on the basis of experimental findings and of mathematical methods, on the basis of the outlined physical models;

[Applying knowledge and understanding]

- assess similarities and differences between physical systems, methodologies to be applied, approximations and mathematical methods to be used;

- apply knowledge and understanding by demonstrating ability to solve exercises and problems of classical mechanics and thermodynamics;

[Learning skills]

- interpret and understand the content of basic texts on topics of classical mechanics and thermodynamics;

- utilize the methodological approach of the Newtonian formulation of Mechanics as a conceptual basis for the formalization of topics in Physics addressed in more advanced courses;

[Making judgments]

- recognize and draw connections not only between different parts of the course but also with the basic concepts acquired in other courses (for example maths and chemistry) for developing an ability for autonomous judgment based on an enlarged knowledge of the various aspects of the problem under consideration;

- evaluate critically the validity limits of the developed models;

[Ability to communicate]

- communicate the product of this study in a clear, synthetic and effective manner, using the correct jargon of Physics, in order to translate correctly even complex concepts in understandable language.

## Prerequisites

• Working knowledge of high school level algebra and trigonometry; • Working knowledge of differential and integral calculus • Principles of analytical geometry and of elementary vector analysis

## Course unit content

Part I

1. Mechanics: introduction and vector calculus

2. Kinematics of material point: one-dimension

3. Kinematics of material point: two- and three-dimension

4. Dynamics of material point: force and Newton’s laws

5. Applications of Newton’s laws

6. Relative motion

7. Work and mechanical energy

Part II

8. Dynamics of the systems of material points I

9. Dynamics of the systems of material points II

10. Dynamics of the rigid body I

11. Dynamics of the rigid body II: statics and rolling motion

12. Energy conservation

13. Collisions

Part III

14. Gravitation: phenomenology and Newton’s law

15. Statics and dynamics of ideal fluids

16. Oscillatory and wave phenomena

17. Thermology and ideal gases

18. Heat and first law of thermodynamics

19. Applications of the first law of thermodynamics

20. Second law of thermodynamics and entropy

Part IV (only for students of the Degree in Physics)

21. Additions on the dynamics of the systems

22. Additions on Gravitation

23. Essentials on the mechanical properties of solids and real fluids

24. Elastic waves

25. Additions on the properties of gases and thermodynamics

26. Special relativity theory: kinematics and dynamics

## Full programme

[provisional version]

Part I [3 CFU]

1. Mechanics: introduction

Classical Mechanics and Thermodynamics; Physics and measurements; physical quantities and units. Basic vector operations: general properties of vectors; unit vectors; vector components; dot product and cross product; rectangular coordinates in 2-D and 3-D; vector derivatives.

2. Kinematics of Material Point: one-dimension

Material Point scheme. Position, velocity, acceleration vectors: constant-velocity and constant-acceleration motion. Free body fall. Harmonic motion.

3. Kinematics of Material Point: two- and three-dimension

Cartesian and polar coordinates representation, intrinsic representation of trajectory, position, velocity and acceleration. Planar motions: projectile motion; circular motion; centripetal acceleration; angular Kinematics.

4. Dynamics of material point: Force and Newton’s laws

Interactions, the conception of force; Newton’s laws; inertial reference systems; mass and weight; linear momentum and its conservation, general form of the Newton’s 2nd law, impulse and impulse theorem, angular momentum and its conservation, theorem of angular momentum.

5. Applications of Newton’s laws

Contact forces: tension, normal force; forces of static and dynamic friction; elastic force and Hooke’s law. Dynamics of the uniform circular motion: centripetal force. Simple pendulum and conical pendulum.

6. Relative motion

Inertial frames of reference: Galilean relativity. Non-inertial frames of reference, fictitious forces. Rotating frames of reference: Coriolis’ force. The earth frame of reference. Roto-translational motion.

7. Work and mechanical Energy

Work of a constant and of a variable force; work-energy theorem for a particle. Power. Conservative and non-conservative forces; potential energy: elastic, gravitational; mechanical energy and its conservation in isolated conservative systems.

Part II [3 CFU]

8. Dynamics of the systems of material points I

System of material points, centre of mass and its motion; theorem of centre of mass motion; linear momentum and its conservation; centre of mass reference system; work-energy theorem. Koenig theorem for kinetic energy; kinetic energy and reference frames.

9. Dynamics of the systems of material points II

Angular momentum of a system of particles; theorem of angular momentum; angular momentum and frames of reference; Koenig theorem for angular momentum. Angular momentum conservation. Dynamics fundamental equations and Newton’s third law.

10. Dynamics of the rigid body I

Discrete and continuous system; rigid body scheme, density, centre of mass; translation, rotation and roto-translation: kinematics of rigid bodies; moment of inertia; Huygens-Steiner’s theorem; axial angular momentum, precession of angular momentum; law of motion for rigid rotation around a fixed axis.

11. Dynamics of the rigid body II: statics and rolling motion

System of parallel forces and centre of gravity. Static equilibrium of a rigid body. Rolling motion of rigid bodies. Work and kinetic energy in the rotational and roto-translational motions.

12. Energy conservation

Generalization of the principle of conservation of mechanical energy; work of external forces; internal energy for a system of particles; energy conservation for a system of particles; energy associated to the centre of mass.

13. Collisions

Definition of collision; impact forces; impulse and impulse theorem; conservation principles in collisions; one-dimensional elastic collisions; inelastic collisions; angular impulse, moment of body impulse; collisions between particles and rigid bodies.

Part III [3 CFU]

14. Gravitation: phenomenology and Newton’s law

Motion of planets and satellites: Kepler laws; Newton’s gravitation law; measurement of constant G; inertial and gravitational mass; gravity near the Earth surface. Spherical distribution of mass (shells theorems). Gravitational potential energy, escape velocity: motion of artificial satellites. Central forces.

15. Statics and dynamics of ideal fluids

Static equilibrium of a fluid; Stevin and Pascal laws; atmospheric pressure: barometric equation; Archimedean principle and buoyancy.

16. Oscillatory and wave phenomena

One-dimensional oscillating systems; simple harmonic motion; energy in the simple harmonic motion; connection with the uniform circular motion; applications: simple, physical and torsion pendulums; damped free oscillations; forced oscillations and resonance. Wave and wave function; phase and phase velocity; harmonic waves, plane waves; D’Alembert equation and its solutions; superposition principle; interference of harmonic waves; standing waves; beats.

17. Thermology and gases

Thermodynamic system and coordinates; equations of state; thermodynamic processes. Zero-th law of thermodynamics, thermal equilibrium. Temperature: scales and methods of measurements. Thermal expansion of solids. Macroscopic properties of gases. Kelvin temperature scale. Equation of state of an ideal gas. Constant-volume gas thermometer. Kinetic theory of gases: pressure and temperature of ideal gases.

18. Heat and first law of thermodynamics

Joule experiments; mechanical equivalent of heat. Reversible and irreversible processes. Heat; specific, molar and latent heat. Phase transitions. Calorimetry. Heat propagation. Work in thermodynamic processes. First law of thermodynamics.

19. Application of first law of thermodynamics

Examples: thermodynamic processes and cycles. Internal energy of an ideal gas. Molar heat of ideal gases. Molecular degrees of freedom and theorem of energy equipartition. Mayer relation. Isothermal, isobaric, isochoric and adiabatic process of an ideal gas.

20. Second law of thermodynamics and entropy

Heat engines and heat pumps. Thermal efficiency. Kelvin-Planck and Clausius enunciations of second law. Reversible Carnot cycle. Thermal efficiency of the Carnot cycle. Carnot’s theorem. Absolute temperature scale. Clausius’ theorem. Definition of entropy. Entropy and second law: the entropy-increase principle. Examples of determination of entropy variation for reversible and irreversible processes.

Part IV [3 CFU] (only for students of the Degree in Physics)

21. Additions on the dynamics of the systems and rigid body

Two-bodies system: relative velocity and acceleration; momentum and energy; motion equation. Variable-mass systems; rocket equation. Short account on precessional motion of rigid bodies: gyroscopes, spinning top; nutation.

22. Additions on Gravitation

Orbits and Kepler’s laws; energy and orbits. Short account on gravitational field and potential, Gauss’s theorem and its application to the problem of spherical mass distribution.

23. Essentials on the mechanical properties of solids and real fluids

Compression and tension, generalized Hooke’s law; Poisson law, volume deformation; shear deformation; torsion and torsion balance; uniform compression, pressure. Surface tension; Laplace formula; capillary phenomena; Jurin’s law. Laminar flow; viscosity; Hagen-Poiseuille law; turbulent flow, Reynolds number; motion of a body immersed in a fluid; mean resistance.

24. Elastic waves

Propagation of a transverse wave on a string; standing waves on a string, harmonic series. Propagation of a pressure longitudinal wave in a gas; sound speed; sound wave intensity; standing longitudinal waves.

25. Additions on the properties of gases and thermodynamics

Kinetic theory of gases: Mean free path of molecules and molecular speed distribution. Third law of thermodynamics. Short account on the statistical interpretation of entropy.

26. Special relativity theory: kinematics and dynamics

Problems of classical physics: time, length, speed, energy, light; postulates of special relativity; consequences of the postulates: relativity of time and length; relativistic velocity addition. Lorentz transformations; Measurement of the space-time coordinates of an event; relativistic velocity transformation; relativity of simultaneity. Collisions and relativistic momentum conservation; relativistic mass and energy; conservation of energy.

## Bibliography

Suggested textbooks Fisica Generale. Meccanica – Termodinamica P. Zotto, S. Lo Russo, P. Sartori I edizione Edizioni La Dotta, Casalecchio di Reno (Bologna), 2016 ISBN 978-88-98648-37-5 Fisica Generale: Meccanica e Termodinamica S. Focardi, I. Massa, A. Uguzzoni e M. Villa II edizione Casa Editrice Ambrosiana (CEA), Milano, 2014 ISBN 978-8808-18215-9 Elementi di Fisica – Meccanica - Termodinamica P. Mazzoldi, M. Nigro e C. Voci II edizione Edizioni Scientifiche ed Universitarie (EdiSES), Napoli, 2008 ISBN: 9788879594189 FISICA 1 Meccanica - Acustica - Termodinamica R. Resnick, D. Halliday, K. S. Krane V edizione Casa Editrice Ambrosiana (CEA), Milano, 2003 ISBN 978-8808-08611-2 Note on textbook choice The textbooks are obviously alternative, although in part complementary. The students must make the choice based on personal preferences and previous preparation: the Resnick is less formal and with a ”tutorial" style, with many exercises and examples; the Focardi and the Zotto are most formally accurate, with some examples and a few or nothing exercises; the Mazzoldi, while presenting examples and exercises, is rather synthetic though preserving a formal exactness.

## Teaching methods

The teaching methodology will be based primarily on frontal lecturing, with help of audio-visual multimedia instruments. The slides used to support lessons will be uploaded weekly on the Elly platform. To download slides, you need to enrol in the online course. The second part of the lesson will normally be devoted to the solution of problems and exercises, under the supervision of the teacher. A selection of exercises and problems for each topics will be uploaded weekly on the Elly platform.

## Assessment methods and criteria

Evaluation methods:

The assessment of the acquisition of learning outcomes will take place through mid-term exams in written form and a final exam in oral and (if necessary) written form. A provisional grade will be proposed to the students if the comprehensive grade of the mid-term exams is above a specific threshold (average grade equal to or higher than 18/30). In order to sustain the oral exam, which will aim to assign the final grade, students must enrol for it (registration to the oral exam on the ESSE3 web platform). The exemption from the written test examination and the assigned provisional grade will retain their validity for all the exams of the 2017/18 academic year (from June 2018 to February 2019).

The final exam, in written and oral form, is mandatory for the students having an insufficient grade of mid-term exams or do not giving the intermediate exams. In such a case will be considered eligible for the oral exam the students who reach for the written exam an assessment equal to or greater than 18/30.

During each of the written mid-term exams, the student will be asked to:

- demonstrate the knowledge and understanding of specific course topics, through open questions (typically 4-5), which will require the use of the technical correct jargon of Physics and synthesis skills (total weight 15 points);

- demonstrate the ability to apply knowledge and understanding by solving some problems (typically 2-3) related to specific course topics (total weight 15 points).

The written mid-term exams will be evaluated in 30-point scale. Each written exam will last 2.5 hours and will have to be done without the help of notes or books. The results of written exams will be notified by posting them on the ESSE3 web platform.

The written final exam will have a similar structure but problems and questions will cover all the topics of the course program.

During the oral exam, the student will be asked to:

- demonstrate the development of an autonomous judgment based on the knowledge and understanding of the fundamental laws of classical mechanics and of thermodynamics, by discussing the carried out written exams (final or mid-term) and deepening of theoretical arguments, drawing connections between the various parts and with basic concepts acquired in other courses;

- be able to use the correct technical-specialist language of Physics so that complex concepts can be translate correctly into an understandable language.

The oral exam will be evaluated in 30-point scale. The final grade will result from the arithmetic mean of the grades of written final exam (or written mid-term exams) and oral exam.

## Other information

Office hours: Wednesday, 10.30-11.30 or upon appointment