Mechanics - part 1
Introductory topics
Presentation of the course, rules of the exam, reference texts.
Metrology, physical quantities, measurements and units of measurement. Fundamental and derived quantities. The International System of Units (SI). Samples for time, mass and length. Precision and significant digits. Dimensional analysis.
Vectors
Vector calculus. Definition of displacement vector. Description of a vector in two and three dimensions. Sum and difference of vectors and their properties. Products of vectors.
Kinematics of the material point in one dimension
Kinematics, one-dimensional motion, trajectory, reference systems, position. Definition of average and instantaneous speeds. Derivatives. Definition of average and instantaneous accelerations. Examples of linear motions. Uniformly accelerated motions. Relation between speed and position in a uniformly accelerated motion. Bodies in free fall. Gravity acceleration measurements.
Kinematics of the material point in three dimensions
Position, speed and acceleration in three dimensions. Instantaneous acceleration vector. Motions with constant acceleration. Falling bodies. Relations between vertical and horizontal speeds. Relations between the positions on vertical and horizontal axes. Range of a projectile. Uniform circular motion. Vector acceleration in a uniform circular motion. Centripetal acceleration. Polar coordinates and polar vectors.
Rotational kinematics
Centripetal and tangential accelerations in curvilinear motions. Relative motions of systems in uniform translational relative motion. Vector nature of speed and acceleration. Reference systems in relative translational motion. Examples. Rotational motion and rototranslatory motion. Rotational variables. Rotation with constant angular acceleration. Vector character of rotational quantities. Relationship between linear and angular variables: scalar and vector forms.
Newton's forces and laws
Particle dynamics. Intuitive evidences and pre-Galilean theories. Inertia. Inertial and non-inertial systems. Operational definition of Force. Vector characteristics of forces. Definition of inertial mass and its dynamic measurement. Second law of dynamics. Third principle of dynamics. Action and Reaction. Difference between mass and weight, weightlessness condition. Static measurement of the inertial mass..
Mechanics - part 2
Dynamics of the material point
Fundamental forces of nature. Empirical forces, static and dynamic sliding friction. Examples of particle dynamics in presence of friction. Dynamics for a uniform circular motion. Forces depending on time, position and speed. Solution of the equation of motion with time-dependent forces. Viscous friction. Solution of the motion of the falling body, regime speed.
Work and energy
Definition of work for constant forces and rectilinear displacements. Work as a scalar product. Physical definition and intuitive concept of work. Work for simple machines. Work of a variable force on a rectilinear displacement. Work of a spring. General definition of work as a line integral in space.
Conservation of mechanical energy
Work-energy theorem for a particle. Kinetic energy, examples of application of the theorem. Definition of power. Conservative and non-conservative forces. Definitions, equivalence of definitions. Definition of potential energy. Exchange of potential and kinetic energy in conservative systems. Definition of mechanical energy and conservation theorem. Systems with different conservative forces. One-dimensional conservative systems. Elastic and gravitational potential energy. Relationship between potential energy and conservative force. Graph of potential energy in one-dimensional systems. Systems with non-conservative forces. Particle systems and internal energy.
Particle systems
Dynamics of particle systems. Definition of the center of mass. Motion law of the center of mass for two particles. Motion law of the center of mass for a system of N particles. Calculation of the position of the center of mass as a volume integral. Definition of momentum for a particle and a particle system. First cardinal equation of dynamics. Preservation of the quantity of motion and examples. Dynamic and energetic approach to particle systems. Impulse and theorem of the impulse. Impulsive forces and examples.
Rotation dynamics - angular momentum
Definition of torque. Definition of angular momentum of a particle. Angular motion law of a particle. Angular momentum of a particle system. Second cardinal equation of systems dynamics. Analogy between the law of translation and the law of rotation. Projection of the PSSC clip: the angular pulse as a vector quantity, and commentary. Angular velocity and angular momentum, discussion of parallelism. Definition of moment of inertia of a particle system. Symmetrical and non-symmetrical systems. Dynamic effects in case of non-parallelism between the angular momentum and angular velocity. Rotation of rigid bodies around a fixed axis. Law of angular motion. Moment of inertia for different geometric solids. Law of conservation of the angular momentum.
Electromagnetism - part 1
Electric charge and Coulomb's law - The electric field
Introduction to electromagnetism. The electric charge. Electrostatic induction phenomena and its applications. Conductors and insulators. The law of Coulomb. Definition of the dielectric constant of the vacuum. The electric field. Calculation of the electric field from discrete distributions of charges. The electric dipole field. Lines of force of the electric field. Principle of superposition, quantization and conservation of the charge. Examples. Calculation of the electric field for continuous distributions of electric charges. Field of a charged plane and a charged wire. Motion of a charged particle in an electric field. Examples: corona discharge, inkjet printer, electrostatic precipitator. Dynamic and energetic behavior of a dipole in an electric field. Mechanical moment and potential energy.
The law of Gauss
Flux of a vector field. Flux of an electric field through a closed surface. Wells and charge sources, statement of the Gauss law for the electric field. Demonstration of the Gauss law. Isolated charged conductor, charge distribution. Electric field on the surface of a conductor. Applications of the law of gauss. Infinite charged wire and plane. Shell and spherical charge distribution. Experimental tests of the inverse square law of the distance.
The electric potential
Potential energy of an electrostatic field. Potential energy of two point charges. Potential energy of a system of charges. Electric potential for a distribution of charges. Calculation of the potential given the electric field. Potential of a point charge, potential of a system of discrete charges. Potential of continuous distributions: charged ring and disk. Equipotential surfaces. Calculation of the electric field given the potential. The gradient operator.
Capacitors
Conductors as equipotential volumes. Surface charge density and curvature radius. Capacitors and definition of the capacitance. Calculation of the capacitance of a capacitor. Parallel plate capacitor. Cylindrical and spherical capacitors. Capacitors in series and in parallel. Energy stored in a capacitor. Capacitors with dielectrics. Dielectrics from an atomic point of view. Gauss's law in dielectrics, examples.
Electric current and resistance
Definition of the electric current and current density. Relationship between current density and drift rate. Calculation of the electron drift velocity in metallic conductors. Resistance, resistivity, conductivity. Ohm's law, microscopic point of view. Energy transfer in circuits.
Electromagnetism - part 2
Magnetic field
Evidence of magnetic phenomena. Magnetic force on a moving charge and definition of the magnetic field. Unit of measurement of the magnetic field. Lorentz force, the speed selector. Motion of a charge in a uniform magnetic field. The cyclotron and particle accelerators. Magnetic bottles. The northern lights. Hall effect. Sign of charge carriers and carrier density.
The law of Ampere
Magnetic force on currents. Mechanical moment on a loop. Loop in a magnetic field: the magnetic moment, mechanical effect and energy effect. The magnetic dipole. Nuclear Magnetic Resonance. Biot-Savart law. The constant k of the Biot-Savart law. Vacuum magnetic permeability. Applications of the Biot-Savart law: fields produced by a straight line and by a circular loop. Force between two parallel wires. Unit of measurement for the current. Ampère's law, statement and proof. Calculation of magnetic fields with Ampère's law. Solenoids and toroids, calculation of internal and external fields.
Faraday's law of induction
Evidence of magnetic induction phenomena. Flux of the magnetic field. Faraday's law. Examples of the Faraday induction law (coil inside a solenoid). Lenz's law. Experiment with the Lenz law (fall of a magnet in a tube). Eddy currents. Electromotive forces generated by motion. Cut flux. Induced electric fields and static electric fields. The betatron. Induction and relative motion. Example of a coil in motion with respect to a magnetic field. Observation of the effects from two reference systems (fixed with the loop, fixed with the magnetic field). Relationship between the induced electric field in a reference frame and the magnetic field in the other.