## Learning objectives

Knowledge and understanding:

In the framework of this course, students obtain an understanding and knowledge of the fundamental laws of classical Mechanics, including systems dynamics, and of Thermodynamics, with particular focus on kinematics, Newton’s laws and conservation principles. In addition, the course provides students with the knowledge of main aspects of the dynamics of rigid bodies, gravitation, oscillatory and wave phenomena and of the Theory of Special Relativity. The experimental method is the basis for understanding the behaviour of systems and phenomena described above. The most important physical theories will be learned in terms of logical and mathematical structure and experimental evidence.

Applying knowledge and understanding:

After completing the course, the student will be able to assess similarities and differences between physical systems, methodologies to be applied, approximations and mathematical methods to be used and will have acquired the ability to apply knowledge and understanding through exercises and problem solving.

Learning skills:

The course will provide the conceptual basis of the Newtonian formulation of Mechanics, which is introductory to the formalizations described in more advanced courses. In addition to methodological tools, the teaching of Physics 1 provides students with the basic language of Physics, allowing them to read and understand basic and advanced texts on the subject.

Communication skills:

The student acquires the technical correct jargon that allows him both to converse with specialists who translate correctly even complex concepts in an understandable language.

Making judgments:

The student is urged to draw connections between not only between the different parts of the course but also with the basic concepts acquired in other teachings (for example maths) to develop a capacity for autonomous judgment based on an enlarged knowledge to the various aspects of the problem in exam.

## Prerequisites

- Working knowledge of high school level algebra and trigonometry;

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

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

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 rigid body I

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

11. Dynamics of the systems of material points II: angular momentum

12. Energy conservation

13. Collisions

Part III

14. Gravitation: phenomenology and Newton’s law

15. Statics and dynamics of ideal fluids

16. Oscillatory phenomena

17. Wave phenomena

18. Thermology - Ideal gases

19. Heat and 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 and rigid body

22. Additions on Gravitation

23. Elastic properties of solids

24. Properties of real fluids

25. Elastic waves

26. Additions on the properties of gases and thermodynamics

27. Special relativity theory

## Full programme

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. 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.

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

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

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

Motion of a system of particles; centre of mass and its motion; Newton’s 2nd law for a system of particles; conservation of linear momentum; centre of mass reference system; work-energy theorem. Koenig theorem for kinetic energy; kinetic energy and reference frames.

9. Dynamics of the rigid body I

Rigid body scheme, density, centre of mass; translation, rotation and roto-translation; torque and moment of force; moment of inertia; Newton’s 2nd law for rotational motions; Huygens-Steiner theorem.

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

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.

11. Dynamics of the systems of material points II: angular momentum

Angular momentum of a particle, of a system of particles and of a rigid body; theorem of angular momentum; symmetry of bodies; angular momentum and frames of reference; Koenig theorem for angular momentum. Angular momentum conservation.

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 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.

17. Wave phenomena

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.

18. 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.

19. 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. 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. Clausius’ theorem. Entropy and second law: the entropy-increase principle.

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. Elastic properties of solids

Compression and tension, generalized Hooke’s law; Poisson law, volume deformation; shear deformation; torsion and torsion balance; uniform compression, pressure.

24. Properties of real fluids

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.

25. 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.

26. Additions on the properties of gases and thermodynamics

Kinetic theory of gases: Mean free path of molecules and molecular speed distribution. Absolute temperature scale. Examples of determination of entropy variation for reversible and irreversible processes. Short account on the statistical interpretation of entropy.

27. Special relativity theory

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

Teaching methodology:

Frontal lesson with help of audio-visual multimedia instruments. The slides of the lectures will be available course web pages at elly.difest.unipr.it.

A part of the course will be devoted to the solution of problems and exercises, under the supervision of the teacher. A selection of exercises and problems will be posted for each topics on the course web pages at elly.difest.unipr.it.

## Assessment methods and criteria

Evaluation methods:

The evaluation is based on mid-term exams (in itinere evaluations) in written form and a final exam in oral and (eventual) written form. A provisional grade will be proposed to the students if the comprehensive grade of the 4 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 2016/17 academic year (from June 2017 to February 2018).

In the event that a student is not able to participate in one of the four written exams but still has an average rating above the threshold on the remaining 3, he will be exempted from the written exam but the oral examination will include the part of the program (theory and exercises) corresponding to the missed test.

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 students who reach the written test examination an assessment equal to or greater than 18/30.

The 4 written mid-term exams will require the solution of some exercises and problems relating to specific course topics and the answer to some questions on the theoretical aspects of these topics. The written final exam will have a similar structure but problems and questions will cover all the topics of the course program. The oral final exam will consist of the discussion of the carried out written exams (final or mid-term exams) and deepening of theoretical arguments chosen in the whole program.

## Other information

Office hours: Wednesday, 10.30-11.30 or upon appointment