Programme

Vectors and vector calculus: definition of a vector, its representation in cartesian and polar coordinates, carrier, properties, dot product, vector product, mixed product.

Material point kinematics: position, velocity, scalar and vector acceleration of a material point. Centripetal and tangential acceleration. Uniformly accelerated motion, uniform and not uniform circular motion, harmonic motion. speed and acceleration in polar coordinates. Areolar speed.
Law of composition of speeds and accelerations; relative motion.

Mechanics of point systems: the Galileo’s first principle of dynamics and Galileo’s relativity. Inertial reference frame. Second and third law of dynamics. Elastic forces, static and dynamic friction, viscosity; applications.
Transformation of coordinates and laws of composition of speeds and accelerations in general; acceleration of Coriolis.
Inertial reference frame and apparent forces: the centrifugal force and the Coriolis force.
Impulse of a force, quantity of motion and their relationship. The moment of force, the angular momentum and their relationship; central forces and pendulum.
The work of a force, kinetic energy and the theorem of kynetic energy. Conservative forces and potential energy, the law of conservation of mechanical energy.
Universal law of gravitation, potential energy and applications. Inertial mass and gravitational mass. Kepler's laws and their explanation using Newton laws.

Material point systems: the cardinal equations of mechanics. Center of mass, definition, properties and the theorem of the center of mass.
The conservation of the quantity of motion and of the angular momentum in isolated systems. Energy of a point system, the Koenig theorem. Two-point systems: reduced mass.
Collisions between material points: elastic and anelastic collisions.

Mechanics of rigid body: translation and rotation, characteristics and vector representation; decomposition of motion in translation and rotation; arbitrariness of the translation and uniqueness of the rotation. Quantity of motion, angular momentum and kinetic energy of a rigid body. Moment of inertia, Steiner's theorem.
Relationship between angular moment and angular velocity of a rigid body, main axes of inertia. Analysis of the motion in systems with a fixed axis rotation, with a rotation axis moving parallel to itself, with a fixed point; gyroscope, trowel and gyroscopic compass.

Mechanics of fluids: pressure, definition and properties. Fluids at rest: law of Stevin, of Pascal, of Archimedes.
Fluids in motion: mass storage in stationary flow, Bernoulli equation.
Laminar motion, viscosity and the law of flow rate.
Touch upon the turbulent motion and the Reynolds number. The motion of a body in a fluid.

Thermodynamics: temperature and its microscopic meaning, heat, definitons and heat transmission: conduction, convection, irradiation.
Transformations of a thermodynamic system, reversible and irreversible transformations: the work in a transformation.
First law of thermodynamics, internal energy.
Perfect gases and their transformations, real gases, solids and liquids. Transformation between phase states of matter.
Second law of thermodynamics: classic statements, thermal engines; the Carnot engine, the Carnot’s theorem and its generalization; entropy, definition, properties and calculation in transformations of a gas or of simple systems.
Kinetic theory of gases: internal energy and entropy of the perfect gas. Third law of thermodynamics. Thermodynamic potentials: Helmotz free energy and Gibbs free enthalpy, applications. Equation of Clausius-Clapeyron

Elasticity: Hooke's law, Young's module and Poisson coefficient. Volume elasticity, shape elasticity; relationship between elastic constants. Plastic deformations.

Waves: mathematical representation of waves. Transverse waves: waves in the strings; longitudinal waves: compression waves, the sound. Energy of the waves. Doppler effect.

Relativity: Galileo’s relativity and Einstein's relativity: the axioms of special relativity and their consequences, time dilation, length contraction; Lorentz's transformations and speed composition. Mass, energy, impulse and equation of motion in special relativity.

Core Documentation

The recommended textbook is:
C. Mencuccini e V. Silvestrini:
Fisica: Meccanica e Termodinamica
Editor Zanichelli

In addition, for a better understanding of how to apply Physics to specific situations, students should use also one of the two following textbooks:

D. Halliday, R. Resnick, J. Walker:
Fisica I
Casa Editrice Ambrosiana

or

R.A. Serway, J.W. Jewett Jr:
Fisica per Scienze ed Ingegneria vol. 1
Editor EdISES

Type of delivery of the course

Lectures on the theoretical aspect of the topics of the course, with the help of slide and internet only when useful. Exercises on the single topics of the course; the exercises are proposed and solved by the teacher. Tutoring: exercises are proposed to the students that have to solve them; the tutor gives only some help and suggestion; after sometime the tutor or one student show to all how to solve the exercise.

Type of evaluation

Written examination: four problems are proposed on the following topics: point body mechanics, many body mechanics, thermodynamics, mechanic of fluids or elasticity or waves; each problem is numerically quoted (10 the point body mechanics, 10 the many body mechanics, 7 the thermodynamics and 3 mechanics of fluids or waves or elasticity). Oral examination: query are proposed in order to evaluate the comprehension of the theoretical aspect of the discipline, of the correlation between different aspects, and the formal and mathematical aspect of the discipline. The grade is in thirtieths; the written work is positive only with at least a grade of 18 with a minimum of 12 on the mechanics and 6 on the other parts. The oral exam add or subtract a maximum of 3 score to the grade of the written work.

Programme

Vectors and vector calculus: definition of a vector, its representation in cartesian and polar coordinates, carrier, properties, dot product, vector product, mixed product.

Material point kinematics: position, velocity, scalar and vector acceleration of a material point. Centripetal and tangential acceleration. Uniformly accelerated motion, uniform and not uniform circular motion, harmonic motion. speed and acceleration in polar coordinates. Areolar speed.
Law of composition of speeds and accelerations; relative motion.

Mechanics of point systems: the Galileo’s first principle of dynamics and Galileo’s relativity. Inertial reference frame. Second and third law of dynamics. Elastic forces, static and dynamic friction, viscosity; applications.
Transformation of coordinates and laws of composition of speeds and accelerations in general; acceleration of Coriolis.
Inertial reference frame and apparent forces: the centrifugal force and the Coriolis force.
Impulse of a force, quantity of motion and their relationship. The moment of force, the angular momentum and their relationship; central forces and pendulum.
The work of a force, kinetic energy and the theorem of kynetic energy. Conservative forces and potential energy, the law of conservation of mechanical energy.
Universal law of gravitation, potential energy and applications. Inertial mass and gravitational mass. Kepler's laws and their explanation using Newton laws.

Material point systems: the cardinal equations of mechanics. Center of mass, definition, properties and the theorem of the center of mass.
The conservation of the quantity of motion and of the angular momentum in isolated systems. Energy of a point system, the Koenig theorem. Two-point systems: reduced mass.
Collisions between material points: elastic and anelastic collisions.

Mechanics of rigid body: translation and rotation, characteristics and vector representation; decomposition of motion in translation and rotation; arbitrariness of the translation and uniqueness of the rotation. Quantity of motion, angular momentum and kinetic energy of a rigid body. Moment of inertia, Steiner's theorem.
Relationship between angular moment and angular velocity of a rigid body, main axes of inertia. Analysis of the motion in systems with a fixed axis rotation, with a rotation axis moving parallel to itself, with a fixed point; gyroscope, trowel and gyroscopic compass.

Mechanics of fluids: pressure, definition and properties. Fluids at rest: law of Stevin, of Pascal, of Archimedes.
Fluids in motion: mass storage in stationary flow, Bernoulli equation.
Laminar motion, viscosity and the law of flow rate.
Touch upon the turbulent motion and the Reynolds number. The motion of a body in a fluid.

Thermodynamics: temperature and its microscopic meaning, heat, definitons and heat transmission: conduction, convection, irradiation.
Transformations of a thermodynamic system, reversible and irreversible transformations: the work in a transformation.
First law of thermodynamics, internal energy.
Perfect gases and their transformations, real gases, solids and liquids. Transformation between phase states of matter.
Second law of thermodynamics: classic statements, thermal engines; the Carnot engine, the Carnot’s theorem and its generalization; entropy, definition, properties and calculation in transformations of a gas or of simple systems.
Kinetic theory of gases: internal energy and entropy of the perfect gas. Third law of thermodynamics. Thermodynamic potentials: Helmotz free energy and Gibbs free enthalpy, applications. Equation of Clausius-Clapeyron

Elasticity: Hooke's law, Young's module and Poisson coefficient. Volume elasticity, shape elasticity; relationship between elastic constants. Plastic deformations.

Waves: mathematical representation of waves. Transverse waves: waves in the strings; longitudinal waves: compression waves, the sound. Energy of the waves. Doppler effect.

Relativity: Galileo’s relativity and Einstein's relativity: the axioms of special relativity and their consequences, time dilation, length contraction; Lorentz's transformations and speed composition. Mass, energy, impulse and equation of motion in special relativity.

Core Documentation

The recommended textbook is:
C. Mencuccini e V. Silvestrini:
Fisica: Meccanica e Termodinamica
Casa Editrice Ambrosiana

In addition, for a better understanding of how to apply Physics to specific situations, student should use also one of the two following textbooks:

D. Halliday, R. Resnick, J. Walker:
Fisica I
Casa Editrice Ambrosiana

or

R.A. Serway, J.W. Jewett Jr:
Fisica per Scienze ed Ingegneria vol. 1 - Quarta Edizione
Casa Editrice EdISES

Type of delivery of the course

Lectures on the theoretical aspect of the topics of the course, with the help of slide and internet only when useful. Exercises on the single topics of the course; the exercises are proposed and solved by the teacher. Tutoring: exercises are proposed to the students that have to solve them; the tutor gives only some help and suggestion; after sometime the tutor or one student show to all how to solve the exercise.

Type of evaluation

Written examination: four problems are proposed on the following topics: point body mechanics, many body mechanics, thermodynamics, mechanic of fluids or elasticity or waves; each problem is numerically quoted (10 the point body mechanics, 10 the many body mechanics, 7 the thermodynamics and 3 mechanics of fluids or waves or elasticity). Oral examination: query are proposed in order to evaluate the comprehension of the theoretical aspect of the discipline, of the correlation between different aspects, and the formal and mathematical aspect of the discipline. The grade is in thirtieths; the written work is positive only with at least a grade of 18 with a minimum of 12 on the mechanics and 6 on the other parts. The oral exam add or subtract a maximum of 3 score to the grade of the written work.