## Unit PHYSICS

- Andrea Orecchini - Didattica Ufficiale

- 42 ore - Didattica Ufficiale - Andrea Orecchini

- G. Ruffo, Fisica per Moduli (2 volumes).

Basic knowledge of algebra: manipulation of numerical and formal expressions, solution of first and second degree equations. Basic knowledge of mathematical analysis: elementary functions such as polynomials, trigonometric functions, exponential and logarithmic functions.

Important prerequisites.

Basic knowledge of mathematical analysis: derivative of elementary functions, derivation rules for composite functions, the concept of integration and integrals of elementary functions. Basic knowledge of vectorial analysis: the concept of vector, scalar product and vector product.

Each test is composed of about twenty question, one third of which encompasses theoretical questions and two thirds encompass numerical exercises.

The questions range over the whole program of the lectures.

During the written exam, it is only allowed to use the questionnaire sheet, paper sheets provided by the teacher, a calculator. It is not allowed the use of mobile phones, personal notes, textbooks.

Physics and the experimental method. Physical quantities and units of measurement. International System. Dimensional equations. Scalars and vectors. Basic elements of vectorial analysis.

Kinematics of the point mass. Average and instantaneous speed. Average and instaneous Acceleration. Calculation of the law of motion starting from the knowledge of the time dependence of the instantaneous velocity: general references to integral calculus and its physical-geometric significance. Law of motion for uniform linear motion and uniformly accelereted linear motion. Uniform circular motion, centripetal acceleration, law of motion.

First principle of dynamics (inertia). Mass, second principle of dynamics and force. Third principle of dynamics (action and reaction). Gravitational force. Weight. Elastic force. Static and dynamic friction forces. Viscous friction forces. General problem of dynamics. Motion under the action of an elastic force. Simple pendulum. General considerations on the harmonic motion.

Definition of work in the case of constant force. Considerations and examples on positive work, negative work, null work. Unit of measure of work. General definition of work in the case of variable force. Definition of power and its unit of measure. Kinetic energy and kinetic energy theorem. Example of application of the kinetic energy theorem to a mass under the action of weight along three paths of remarkable interest. Work done by some important forces along a closed path: weight, elastic force, friction. Conservative and non-conservative forces. Definition of potential energy. Definition of mechanical energy and theorem of conservation of mechanical energy.

Electrostatic phenomena. Power and electrical charges. Microscopic electric structure of matter and atoms. Additivity of electric charges. Insulators and conductors. Coulomb law. Dielectric constant of vacuum and relative dielectric constant. Comparison between Coulomb force and gravitational force. Electric field. Superposition principle (additivity electrical force and electric field). Exercise on the superposition principle: field of an electric dipole. Flux of a vector through a surface. Solid angle. Gauss theorem. Some applications of the Gauss theorem: field of a uniformly charged insulating sphere, field of a uniformly charged infinite plane, field of a double charged plane. Work of the electrostatic force generated by a point charge. Electrostatic potential energy. Electrical potential. Potential energy and electrical potential of a parallelel-plates capacitor. Electrostatics in conductors. Electromotive force and electric current. Ohm's law, resistance and conductivity. Resistors in series and resistors in parallel. Joule effect. Resistivity. Alternating current and effective power.

Elementary magnetic phenomena. Oersted's and Ampère's experiments. Second Laplace law and Lorentz force. Magnetic induction field. Motion of a charged particle in a uniform magnetic field. Mass spectrometer. Biot and Savart law. Magnetic permeability of vacuum and relative magnetic permeability: diamagnetic, paramagnetic and ferromagnetic materials. First Laplace law. Magneti field and magnetic moment of a current loop. Field of a solenoid. Notes about magnetic induction.

Density and pressure in a fluid. Continuity equation and flow rate. Bernoulli's equation and some of its consequences: hydrostatic paradox, Archimedes' force, Venturi effect.

Measurement methods: direct and indirect measurements. Systematic errors, statistical errors, instrumental sensitivity. Mean value as best estimate of a measured quantity. Variance, standard deviation and standard deviation of the mean. Distribution about the mean value of repeated measurements. Event count measurements, Poisson distribution and standard deviation. Independent errors, gaussian distribution, standard deviation and confidence intervals. Error propagation. Remarkable examples: sum and difference, product and quotient. Squared propagation for independent errors. General formula for error propagation by means of partial derivatives.