Teachings

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Professor
FRANCESCO DETTORI (Tit.)
PIERLUIGI BORTIGNON
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

Welcome to the General Physics 1 course, the first physics course of the Bachelor's degree in Mathematics.

The course aims to provide students with the fundamentals on physical phenomena of mechanics, including fluids and oscillations, as well as the thermodynamics.
Topics will be treated from the classical point of view, however, references to a more updated view will be made.

Being the first course in Physics, more general topics will also be addressed such as the concept of scientific measurement and therefore its uncertainty.

Examples and "classic" exercises of basic physics will be used as well as hints on the basic mechanisms of these processes in light of the knowledge of current physics.

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

1. General concepts. Measurements, models, theories. Physics quantities. Space and time. Vectors and scalars. Vector operations.

2. Kinematics and forces. Average velocity and instantaneous velocity; acceleration. One dimensional motion. Two-dimensional motions. Harmonic motion. Dynamics of point particles force and mass; Newton laws. Reference systems; Galileian transforms and limitations; non-inertial reference frames; Centrifugal and Coriolis force. Friction.

3. Work and energy. Work for constant and variable forces; kinetic energy; kinetic energy theorem. Conservative forces; potential energy. Potential energy diagrams. Mechanical energy conservation.

4. Gravitation. Newton's law of universal gravitation. Kepler's laws. Force and potential energy for a homogeneous sphere.

5. Impulse and linear momentum. Impulse and linear momentum change for point particles. Momentum conservation for point particles. Variable mass systems. Elastic and inelastic collisions.

6. Rotational motion. Rotational variables: angular velocity and acceleration. Torque and angular momentum. Kinetic energy and moment of inertia. Rigid bodies. Angular momentum conservation; spinning top and gyroscope. Equilibrium of rigid bodies.

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.

The lectures by the teachers will be standard, with
introduction of key concepts of Physics I, demonstrations of theorems and resolutions of typical examples and applications.
The teaching material will consist of the notes taken from the
students, from possible transparencies (only where necessary) and obviously from recommended textbooks.

The tutorials carried out by the tutors will instead be more focused on
more important exercises to be familiar with the resolution of
problems of Physics I.

Verification of learning

Two written tests will take place in the evaluation (one in mid-semester and the other after the end of the course) and an oral exam.
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.

For those absent at intermediate written tests, a final written test will be scheduled.

Texts

This is the reference text:
Fisica 1 - Halliday-Resnick-Krane (Ambrosiana)

Other books are used in some specific parts of the course (we will refer to them explicitly in due time):

- Feynman Lectures in physics
- Fisica - Mazzoldi, Nigro, Voci
- Barone - Relativity

More Information

In general, the comprehension of Physics cannot be done through a mnemonic study of a single textbook.
We therefore advise students to read also other textbooks (even very basic) in order to understand the basics concepts and in order to find new lists of exercises.

We suggest to perform the "mini-experiments" suggested during lectures in order to have confidence on the physics phenomena at a practical level rather than abstract. For experiments which cannot be done "at home" we suggest to have a look at the large video collection on the web (e.g. youtube) to be watched with a critical eye.

Questionnaire and social

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