The course introduces the scientific method. the first part of the course presents newton's mechanics. The student becomes familiar with the basic models of classical physics and, in particular, with such concepts as physical quantity, field, conservation law. The vector algebra is discussed as well. The second part of the course is dedicated to thermodynamics with the presentation of its general principles, focusing the attention to the perfect gas case. The student is able to apply the above concepts to the solution of simple problems by means of appropriate analytical procedures.

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teaching materials

Introduction to kinematics: Position and time law of a material point. Degrees of freedom of a mechanical system.

Scalars and vectors: Position vector and vector spaces. Cartesian components and polar components. Applied vectors and free vectors. Product of scalar and vector and sum of vectors. Difference between vectors. Vectors under rotation of the Cartesian reference system. Dot product and vector product of vectors. Vector product and mixed product of vectors.

Kinematics: time law and trajectory of the motion of a material point. Displacement vector and mean velocity vector. General rectilinear motions, speed, link between time law and instantaneous speed. Uniform rectilinear motion. Average and instantaneous acceleration and link with the time law.

Uniformly accelerated motion in a straight line. Vertical motion of a grave. Simple harmonic motion.

Introduction to ordinary differential equations: direct first order differential equations and with separable variables. Linear ordinary differential equations: general properties. Solutions for first and second order linear equations.

Rectilinear motion exponentially damped and with acceleration as a function of position. Relative rectilinear motions. Instantaneous velocity vector in space motions.

Curvilinear coordinate and polar components of the velocity vector in space and in the plane. Instantaneous acceleration vector and its Cartesian and intrinsic decompositions.

Intrinsic representation of instantaneous acceleration and its relationship with the Cartesian representation. Osculatory circle and curvature of a trajectory in the plane.

Uniform circular motion. Non-uniform circular motions. Case of angular acceleration as a function of angle. Harmonic circular motion.

Parabolic motion of a body with different initial conditions. Acceleration in intrinsic representation and radius of curvature in the parabolic motion of a body.

Introduction to dynamics and first principle. Introduction to the concept of force. Second Principle of dynamics: the different formulations, the meaning and the law of motion. Third law of dynamics.

Impulse theorem and mean force in a time interval.

Resultant of multiple forces.

Static equilibrium for a material point. Weight force. Binding reactions.

Fundamental forces of nature.

Weight force near the earth's surface and universal gravitational force. Link between inertial mass and gravitational mass.

Constraining forces due to the weight force in systems accelerated with respect to the Earth (problem of the lift in the fall or in ascent). Weight kilogram and exercises on reaction forces in accelerated systems.

Static and dynamic sliding friction with exercises.

Inclined plane with and without friction. Inclined plane and motion of bodies.

Elastic force, ideal springs and harmonic motion.

Viscous friction and motion of a body in a viscous liquid. Fall of a body into the atmosphere.

Force decomposition into tangential and centripetal components with respect to the trajectory.

Frictionless motion on banked curve. Motion with static friction on a flat curve.

Conical pendulum. Simple pendulum and small swing method. Large oscillations and relationship between angular velocity and angle in the simple pendulum.

Ideal wires, pins and pulleys: wire tension and constraint reaction.

Work of a force on a material point moving along a trajectory. Additivity of work and work of the resultant force. Live force theorem and kinetic energy. Particular case of the weight force and introduction of the relative potential energy.

Conservative forces: equivalent definitions. Conservative forces and potential energy. Case of elastic force and in general for position-dependent one-dimensional forces. Conservativity and differential nature of elementary work.

Conservative forces and gradient forces. Meaning of gradient of a function. Local condition of conservation of a force. Conservative forces and zero rotor.

Oscillations from conservative forces: the circular hole and the parallel with the simple pendulum.

Small oscillation method for conservative forces in one dimension.

Moment of a vector and angular momentum of a material point. Moment of force and angular momentum theorem. Angular momentum and momentum theorems for impulsive forces.

Damped harmonic oscillator and application of the theorems of work and mechanical energy. Generalized conservation of energy theorem. Damped harmonic oscillator - forced.

Galilean relativity principle and Galileo's transformations. Non inertial reference frames and apparent forces: case of generic translational motion with respect to an inertial frame.

Non-inertial reference frames: general case of roto-translational motion with respect to an inertial frame. Coriolis force and examples.

Introduction to system dynamics: internal forces and external forces.

First cardinal equation of systems and theorem of conservation of total momentum. Center of mass: position, speed and acceleration. Law of composition of centers of mass.

Second cardinal equation of systems and conservation theorem of the total angular momentum of the system. Pole dependence of the moment of forces.

Reference system of the center of mass of the system. Koenig's first theorem on angular momentum. Koenig's second theorem on kinetic energy.

Kinetic energy theorem for systems. Conservation theorem of mechanical energy and generalized conservation theorem for systems.

Resulting moment of a system of forces applied to different points. Pair of forces and systems of equivalent forces. Systems of parallel forces and the case of the weight force.

Rigid bodies. Local mass density and average density. Center of mass of a rigid body. Parallel forces and gravitational force for a rigid body.

General motion of the rigid body. Purely translational motion. Rotational motion around a fixed axis. Axial moment of inertia and additive properties. Huygens-Steiner theorem.

Calculation of some moments of inertia. Compound pendulum. Conservation laws in rigid bodies. Static equilibrium of rigid bodies.

Binary collisions. Impulsive forces. Completely inelastic collisions and examples. Ballistic pendulum. Linear and in-plane elastic collisions.

Universal gravitation: (i) Kepler's laws and derivation of the gravitational force; (ii) gravitational force and weight force. Physical meaning of Kepler's laws. Gravitational potential energy. Escape velocity.

Introduction to thermodynamics: thermodynamic equilibrium states and systems. State variables. Temperature and thermometry.

Ideal gases and state law. Kinetic theory of ideal gases. Interpretation of thermal equilibrium in the light of kinetic theory.

Definition and measurement of a heat exchange in one-phase systems and in the coexistence of two phases (phase transition). Latent heat of fusion and evaporation. Thermal capacity and specific heat.

Joule's experiment on heat as a form of energy. Work and heat in thermodynamics and their kinetic interpretation.

First law of thermodynamics and its infinitesimal form for reversible transformations.

Specific heats at constant pressure and volume. Applications to ideal gases and Meyer's relation.

Joule's experiment on the free expansion of ideal gases and internal energy.

Reversible adiabatic transformations for ideal gases.

Cyclic thermal machines. Carnot machine and cycle.

Second law of thermodynamics and equivalence between the statements of Kelvin and Clausius. Carnot's theorem. Generalization to cyclic heat machines with more than two heat sources.

Entropy, integral and Clausius theorem.

- Fisica - Meccanica e termodinamica- con esempi ed esercizi, Corrado Mencuccini e Vittorio Silvestrini, Casa Editrice Ambrosiana

Programme

Introduction to the course, scientific method and physical quantities. Space and time.Introduction to kinematics: Position and time law of a material point. Degrees of freedom of a mechanical system.

Scalars and vectors: Position vector and vector spaces. Cartesian components and polar components. Applied vectors and free vectors. Product of scalar and vector and sum of vectors. Difference between vectors. Vectors under rotation of the Cartesian reference system. Dot product and vector product of vectors. Vector product and mixed product of vectors.

Kinematics: time law and trajectory of the motion of a material point. Displacement vector and mean velocity vector. General rectilinear motions, speed, link between time law and instantaneous speed. Uniform rectilinear motion. Average and instantaneous acceleration and link with the time law.

Uniformly accelerated motion in a straight line. Vertical motion of a grave. Simple harmonic motion.

Introduction to ordinary differential equations: direct first order differential equations and with separable variables. Linear ordinary differential equations: general properties. Solutions for first and second order linear equations.

Rectilinear motion exponentially damped and with acceleration as a function of position. Relative rectilinear motions. Instantaneous velocity vector in space motions.

Curvilinear coordinate and polar components of the velocity vector in space and in the plane. Instantaneous acceleration vector and its Cartesian and intrinsic decompositions.

Intrinsic representation of instantaneous acceleration and its relationship with the Cartesian representation. Osculatory circle and curvature of a trajectory in the plane.

Uniform circular motion. Non-uniform circular motions. Case of angular acceleration as a function of angle. Harmonic circular motion.

Parabolic motion of a body with different initial conditions. Acceleration in intrinsic representation and radius of curvature in the parabolic motion of a body.

Introduction to dynamics and first principle. Introduction to the concept of force. Second Principle of dynamics: the different formulations, the meaning and the law of motion. Third law of dynamics.

Impulse theorem and mean force in a time interval.

Resultant of multiple forces.

Static equilibrium for a material point. Weight force. Binding reactions.

Fundamental forces of nature.

Weight force near the earth's surface and universal gravitational force. Link between inertial mass and gravitational mass.

Constraining forces due to the weight force in systems accelerated with respect to the Earth (problem of the lift in the fall or in ascent). Weight kilogram and exercises on reaction forces in accelerated systems.

Static and dynamic sliding friction with exercises.

Inclined plane with and without friction. Inclined plane and motion of bodies.

Elastic force, ideal springs and harmonic motion.

Viscous friction and motion of a body in a viscous liquid. Fall of a body into the atmosphere.

Force decomposition into tangential and centripetal components with respect to the trajectory.

Frictionless motion on banked curve. Motion with static friction on a flat curve.

Conical pendulum. Simple pendulum and small swing method. Large oscillations and relationship between angular velocity and angle in the simple pendulum.

Ideal wires, pins and pulleys: wire tension and constraint reaction.

Work of a force on a material point moving along a trajectory. Additivity of work and work of the resultant force. Live force theorem and kinetic energy. Particular case of the weight force and introduction of the relative potential energy.

Conservative forces: equivalent definitions. Conservative forces and potential energy. Case of elastic force and in general for position-dependent one-dimensional forces. Conservativity and differential nature of elementary work.

Conservative forces and gradient forces. Meaning of gradient of a function. Local condition of conservation of a force. Conservative forces and zero rotor.

Oscillations from conservative forces: the circular hole and the parallel with the simple pendulum.

Small oscillation method for conservative forces in one dimension.

Moment of a vector and angular momentum of a material point. Moment of force and angular momentum theorem. Angular momentum and momentum theorems for impulsive forces.

Damped harmonic oscillator and application of the theorems of work and mechanical energy. Generalized conservation of energy theorem. Damped harmonic oscillator - forced.

Galilean relativity principle and Galileo's transformations. Non inertial reference frames and apparent forces: case of generic translational motion with respect to an inertial frame.

Non-inertial reference frames: general case of roto-translational motion with respect to an inertial frame. Coriolis force and examples.

Introduction to system dynamics: internal forces and external forces.

First cardinal equation of systems and theorem of conservation of total momentum. Center of mass: position, speed and acceleration. Law of composition of centers of mass.

Second cardinal equation of systems and conservation theorem of the total angular momentum of the system. Pole dependence of the moment of forces.

Reference system of the center of mass of the system. Koenig's first theorem on angular momentum. Koenig's second theorem on kinetic energy.

Kinetic energy theorem for systems. Conservation theorem of mechanical energy and generalized conservation theorem for systems.

Resulting moment of a system of forces applied to different points. Pair of forces and systems of equivalent forces. Systems of parallel forces and the case of the weight force.

Rigid bodies. Local mass density and average density. Center of mass of a rigid body. Parallel forces and gravitational force for a rigid body.

General motion of the rigid body. Purely translational motion. Rotational motion around a fixed axis. Axial moment of inertia and additive properties. Huygens-Steiner theorem.

Calculation of some moments of inertia. Compound pendulum. Conservation laws in rigid bodies. Static equilibrium of rigid bodies.

Binary collisions. Impulsive forces. Completely inelastic collisions and examples. Ballistic pendulum. Linear and in-plane elastic collisions.

Universal gravitation: (i) Kepler's laws and derivation of the gravitational force; (ii) gravitational force and weight force. Physical meaning of Kepler's laws. Gravitational potential energy. Escape velocity.

Introduction to thermodynamics: thermodynamic equilibrium states and systems. State variables. Temperature and thermometry.

Ideal gases and state law. Kinetic theory of ideal gases. Interpretation of thermal equilibrium in the light of kinetic theory.

Definition and measurement of a heat exchange in one-phase systems and in the coexistence of two phases (phase transition). Latent heat of fusion and evaporation. Thermal capacity and specific heat.

Joule's experiment on heat as a form of energy. Work and heat in thermodynamics and their kinetic interpretation.

First law of thermodynamics and its infinitesimal form for reversible transformations.

Specific heats at constant pressure and volume. Applications to ideal gases and Meyer's relation.

Joule's experiment on the free expansion of ideal gases and internal energy.

Reversible adiabatic transformations for ideal gases.

Cyclic thermal machines. Carnot machine and cycle.

Second law of thermodynamics and equivalence between the statements of Kelvin and Clausius. Carnot's theorem. Generalization to cyclic heat machines with more than two heat sources.

Entropy, integral and Clausius theorem.

Core Documentation

- Elementi di Fisica - Meccanica e Termodinamica, Paolo Mazzoldi, Massimo Nigro, Cesare Voci - Libro Edises 2022- Fisica - Meccanica e termodinamica- con esempi ed esercizi, Corrado Mencuccini e Vittorio Silvestrini, Casa Editrice Ambrosiana

Reference Bibliography

P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica - Meccanica e Termodinamica, ed. Edises C. Mencuccini, V. Silvestrini, "Fisica - Meccanica e Termodinamica", Ed. AmbrosianaType of delivery of the course

Lessons will be held face-to-face according to the established timetable. Each lesson consists of two academic hours of teaching for four weekly lessonsAttendance

Students are warmly recommended to attend lessons in presence so that the direct interaction with the teacher will permit an optimal didactical effectType of evaluation

The evaluation is done through a written test and an oral test which can be accessed by those who have reached the sufficiency in the written test