66682 - Physics

Learning outcomes

At the end of the course the student must know the basic concepts of Newtonian dynamics and electromagnetism, and has acquired the basics of geometrical and wave optics. She/he can treat physical problems by means of mathematical tools such as differential calculus. She/he has the skills to apply such a knowledge to solve simple physical problems.

Course contents

One-dimensional kinematics. Average and instantaneous velocity.Average and instantaneous acceleration. Linear motion. Linear motion with constant acceleration.

Scalars and vectors. Sum and difference of vectors. Decomposition of vectors with respect to the axes. Unit vectors. Vector components. Sum, difference, and scalar product of vectors by means of vector components.

Motion in two and three dimensions. Motion of projectiles. Circular motion. Relative motion in two dimensions.

Forces and superposition of forces. Principle of inertia. Newton's second law. Some special forces: gravitational, normal, friction, elastic force, centripetal force. Newton's third law. Work of a constant force. Definition of kinetic energy. Work of the gravitational force. Work of elastic force. Power. Potential energy and work. Conservative forces. Gravitational potential energy. Elastic potential energy. Conservation of mechanical energy. Equilibrium points of a system.

Center of mass of system of particles and of an extended body. Newton's second law for a system of particles. Momentum. Conservation of momentum.

Explosions and collisions. Definition of impulse of a force. Collisions between particles. Completely inelastic and elastic collisions. Vector product. Moment of a force. Equilibrium of a rigid body

Rotational motion. Angular velocity. Angular acceleration. Rotational kinetic energy. Moment of inertia. Theorem of parallel axes.

Torque of a force. Newton's Second Law in angular form. Work and rotational kinetic energy. Rolling. Angular momentum. Conservation of angular momentum. Rigid body rotating about a fixed axis.

Simple harmonic motion. Harmonic oscillator. Harmonic oscillator with two masses.

 

Electric charge and electric phenomena. Coulomb's law. Coulomb's law in vector form. Definition of electric field. Electric field generated by a point charge. Field generated by a dipole. Field generated by a flat distribution of charges.

Electric flux. Gauss' law. Relation between Gauss' law and Coulomb's law. Isolated charged conductor. Conducting plane.

Electric potential energy. Definition of electric potential. Calculation of the electric potential by the electric field. Potential in a uniform electric field. Potential generated by a point charge. Calculation of the electric field from the electric potential.

Electrical capacity. Parallel plate capacitor. Capacitors in series and parallel.

Definition of electric current. Current density. Drift velocity of charge carriers

Definition of electrical resistance. First Ohm's law. Definition of specific resistivity. Second Ohm's law. Dependence of resistance on temperature.

Dissipation of heat. Resistors in series and parallel. DC circuits. Electromotive force. Elementary single loop circuit. Kirchhoff's second law. Circuit with more loops. Kirchhoff's first law. Determination of currents and potentials in a circuit. Real batteries and internal resistance of a battery. RC circuits. Charging and discharging a capacitor.

Magnetic phenomena. Definition of the magnetic field. Motion of a charged particle in a uniform magnetic field Lorentz force. Speed controller. Mass spectrometer. Magnetic force on a current-carrying conductor.

Torque on a loop. Definition of magnetic dipole. The magnetic dipole moment of the electron and the proton. Law of Biot and Savart. Magnetic field generated by a straight wire. Force between parallel conductors. Circuital of the magnetic field. Ampere's law. Solenoids.

Geometric optics: Snell's law, spherical and flat mirrors, thin lenses. Ray-tracing, equation of conjugate points, formulas for the magnification. Examples of image formation in mirrors and lenses: magnifying glass, microscope, telescope, prism spectrometer.

Elements of wave optics. Electromagnetic waves as particular solution of Maxwell's equations. Sinusoidal plane waves. Polarization of light: mirages and polaroid filters. Interference between plane waves. Diffraction on a slit. Interference with two slits, gratings. Grating spectrometer: fundamental equation and dispersive power. X-ray diffraction.

Resolving power and dispersion of a diffraction grating.

Readings/Bibliography

Readings/Bibliography

D. Halliday, R. Resnick, J. Walker

Fondamenti di Fisica

Meccanica Termologia Elettrologia Magnetismo Ottica

Sesta edizione

Casa Editrice Ambrosiana

ISBN 978-8808-08797-3

Teaching methods

Class lectures

Assessment methods

During the course students can sit for two written ongoing tests.
The first takes place at approximately midway of the course and is centered on concepts of Newtonian mechanics. The second is carried out upon completion of the course and is centered on optics and electromagnetism. Both tests involve the solution of numeric problems, also accompanied by theoretical questions. Students can use their scientific pocket calculator and consult textbooks and/or notes made available by the lecturer. The average of the two scores of the ongoing assessment gives a final mark. Passing at least one of the two assessments with a score of 17/30 gives access to an oral exam. Students that either failed both assessments or did attend the tests, must  sit for a written test on the entire program. The written exam is considered passed with a final score of at least 17/30, and an oral exam must follow, either in the same or in a later exam session (however, not later than the beginning of the lessons of the physics course in the next year)

Office hours

See the website of Elisabetta Venuti

See the website of Riccardo Tarroni