### Teachings

Select Academic Year:     2016/2017 2017/2018 2018/2019 2019/2020 2020/2021 2021/2022
Professor
PIERLUIGI BORTIGNON (Tit.)
FRANCESCO DETTORI
Period
Second Semester
Teaching style
Convenzionale
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/64]  MATHEMATICS [64/00 - Ord. 2017]  PERCORSO COMUNE 12 96

### Objectives

The course aims to help and push students to expand their knowledge and develop mental tools that will be useful for their careers.

At the end of the course the students should have developed or strengthened their ability to reason and problem-solving, their confidence, autonomy, and technical experience to join successfully in their profession. The reasoning tools learned can help them to take thoughtful decisions in real life situations.

### Prerequisites

1. High school level mathematics: algebra and basic trigonometric formulas. Most of the needed math (elementary calculus) is developed during the course profiting also from the calculus and geometry courses.
2. Physics: there are no pre-requisites.

### Contents

0. General concepts. Scientific method. Reference systems.

1. Kinematics. Graphic analysis. Uniform motions. Uniform circular motion. Periodic motion.

2 Dynamics of a point. Law of inertia. Inertial reference system. Newton's law. Quantity of motion. Action-reaction principle. Work of a force. Kinetic energy. Work calculations. Potential energy. Conservation of energy. Total energy. Central forces theorem. The power.

3. Forces. Frictional force. Static and dynamic coefficient of friction. Viscous resistance and air resistance. Elastic force. Elastic potential energy Diagram of energy in one dimension. Energy graphs for some forces. Harmonic motion.

4. Gravitation. Historical introduction. Kepler's laws. Newton's law of universal gravitation. Gravitational field. Lines of force and equipotential lines. Measurement of the Cavendish constant. Force of gravity of a sphere of mass. Gravitational potential.

5. Mechanics of systems. Torque. Angular moment. Center of gravity. Impulse theorem. Momentum conservation. Elastic / inelastic collisions. First cardinal equation of mechanics. Angular momentum of a system of particles. Second cardinal equation of mechanics. Conservation of angular momentum. Energy of a system of particles.

6. Rigid bodies. Rotation around a fixed axis. Angular momentum theorem with respect to a fixed axis. Moment of inertia. Rotational kinetic energy.

7. Oscillations. Harmonic oscillator: simple, damped and with sinusoidal force. Resonance, power. Systems with two degrees of freedom: coupled oscillators. Systems with an infinite number of degrees of freedom: standing waves; ideas on Fourier transform. Beats.

8. Mechanical waves. Propagation of waves. Wave equation. Dispersion; phase and group velocity. The principle of superposition. Transverse waves in a string. Longitudinal waves in a chain with springs and masses. Sound waves. Generation of sounds and relation to Fourier analysis. The speed of sound. Sound standing waves. Interference. Doppler effect.

9. Fluids. General concepts: fluids and solids. Pressure and density. Pascal and Archimedes' principles. Introduction to fluid dynamics. Bernoulli's equation and applications.

10. Introduction to special relativity. Experimental information. Basic postulates. Synchronization. Lorentz transformations. Consequences and examples. Basics of relativistic dynamics. Energy-mass equivalence.

11. Thermodynamics. Basic concepts: the idea of macrostate and microstate of complex systems. Temperature and heat as energy exchange; thermal equilibrium; thermometers.

12. Calorimetry. Thermal behavior of solid and liquid bodies, gases.
Thermal capacity and specific heat. The first principle of thermodynamics and applications.

13. Perfect gas and absolute temperature. Elements of kinetic theory: the Maxwell-Boltzmann distribution; kinetic interpretation of temperature; theorem of equipartition of energy.

14. Thermodynamic transforms: isothermal, adiabatic. Reversible and irreversible transforms. The second principle of thermodynamics: Kelvin and Celsius statements; thermal engines. Carnot theorem and absolute temperature. Entropy. Third principle of thermodynamics.

### Teaching Methods

The course is structured in lectures and exercises.

Lectures are provided using a blackboard, a tablet, or both, in the classroom or via web streaming remotely.

The teaching material consists of recommended textbook, possible transparencies, and the notes taken from the students.

The tutorials carried out by the tutors are focused on important exercises to become familiar with the resolution of problems of Physics I.

### Verification of learning

Written tests will take place in the evaluation and an oral exam.

Homework assignments, if correct and handed in time, give a bonus in the final grade.

The written tests will mainly evaluate the ability to solve basic physics exercises explained in class and of the same kind of those carried out in the exercises.

The oral test will evaluate the understanding of the elements of Physics.

Tests and exams take place in person in a physical room or remotely using digital tools.

CRITERIA FOR THE DETERMINATION OF THE FINAL GRADE

Homework assignments, if correct and handed in time, give a bonus in the final grade.

The written exam will be evaluated to be admitted to the oral exam
and will contribute to the final grade on the basis of the discussion of its solution during the oral exam
The admission to the oral exam does not automatically imply a positive outcome of the full exam.

The oral exam will verify the acquired or missing competences as observed during the written exam, and will verify the student preparation on the theoretical part of the program, both considering the fundamental notions to be known and the comprehension of the physics itself.

The final grade is expressed in points / 30

### Texts

Main textbooks:
- Fisica. Volume 1 - P. Mazzoldi, M. Nigro, C. Voci (EdiSES)
- Fisica 1 - Halliday-Resnick-Krane (Ambrosiana)