The course will cover basic topics in Mechanics and Electromagnetism: material point kinematics; material point mechanics; work and energy; reference systems and relative motions; system mechanics; rigid body mechanics; electrostatics; electric conductors and currents; magnetism; nonstationary electromagnetic phenomena and electromagnetic waves.
P. Mazzoldi, M. Nigro, C. Voci
ELEMENTI DI FISICA. Meccanica e Termodinamica (III ed.)
(EdiSES Università)
P. Mazzoldi, M. Nigro, C. Voci
ELEMENTI DI FISICA. Elettromagnetismo e Onde (III ed.)
(EdiSES Università)
Notes provided by the professor.
Learning Objectives
The course aims to provide the basic tools and knowledge of Physics necessary to be able to interpret fundamental physical phenomena and solve problems in the areas of mechanics and electromagnetism.
By the end of the course, the student will be able to understand the meaning of physical quantities and fundamental physical laws in the above areas, and will be able to apply theoretical knowledge to modeling and problem solving.
The knowledge and method of work acquired will enable the student to be able to continue in the more advanced Physics and Engineering courses delivered in later years.
Prerequisites
Mastery of basic mathematical knowledge (algebra and trigonometry) and the main results of differential calculus (derivatives, integrals, differential equations) is required. Therefore, it is strongly recommended that the student take the Mathematical Analysis course provided during the first semester.
No prior knowledge of Physics is required.
Teaching Methods
The course will be developed with face-to-face lectures, in which the lecturer will illustrate the topics mainly by making use of a blackboard or electronic tablet connected to a screen. Slides and demonstration videos will also be shown during the lectures, in which the fundamental physical phenomena discussed in the lecture will be exemplified through their direct experimental verification.
Real-time polling applications (e.g., Wooclap) will also be used during the lectures to stimulate students to give an interpretation of the proposed phenomena, in an interactive and anonymous mode.
All course material will be made available on the Moodle e-learning platform, where the following will be uploaded: transcripts of what is written on blackboard/tablet during lectures, slides and videos shown to complement explanations, exam papers (with solutions) assigned in previous years, collections of exercises performed.
Access will also be provided to a collection of video lectures given in previous years that can be used on an optional basis as supplementary material.
On a weekly basis, a reception will be organized (preferably in telematic mode) during which students will have the opportunity to ask direct questions to the lecturer about the organization and content of the course, and request clarification on the performance of problems.
Further information
Type of Assessment
The verification of learning will be done through a written test, the passing of which will allow access to the final oral examination.
WRITTEN TEST:
The written verification will focus on solving physics problems of mechanics and electromagnetism, to be addressed by applying the physical laws and results discussed in class. The correctness and rigor of the development and the ability to obtain and express the results correctly will be evaluated. The student may pass the written test through one of two modes provided:
1) Ongoing partial tests: three exercises will be organized during the semester of teaching, during class time, each covering a limited part of the syllabus. An average mark achieved on the three tests equal to or above 16/30 will allow admission to the oral exam (regardless of any non-sufficient marks on the individual tests).
2) Complete written test: as an alternative to the in-progress tests, at least 7 written tests will be organized during the academic year, during standard examination periods, covering the entire program. A grade of 16/30 or higher will allow admission to the oral exam.
ORAL EXAM:
During the oral examination the student will be asked three questions on the course topics covered during the lectures. The questions will focus on general illustration of the most important quantities and physical laws, performance of demonstrations of the main results, and illustration of notable examples discussed in class. The exposition will normally take place in front of a blackboard and will typically last 25-30 minutes.
The final grade of the oral examination will be based on the grade of the written examination and the evaluation of the interview.
Course program
1) MATERIAL POINT KINEMATICS.
Rectilinear motions. Average velocity and instantaneous velocity. Geometric interpretation of velocity in a graph x(t) and displacement in a graph v(t). Uniform rectilinear motion. Average acceleration and instantaneous acceleration. Uniformly accelerated rectilinear motion. Fall of a grave. Examples of uniform rectilinear motion, uniformly accelerated motion, various motions. Recalls on vectors and operations between vectors: product by a scalar, sum and addition of vectors, decomposition of vectors into components. Scalar product. Vector product. Motion in multiple dimensions. Vector kinematic quantities. Velocity and acceleration in intrinsic coordinates. Parabolic motion. Circular motion: general definitions and relationships between angular and linear kinematic quantities. Uniform and uniformly accelerated circular motion.
2) MATERIAL POINT DYNAMICS.
Material point dynamics. Newton's three laws: formulation and examples. Momentum and momentum of a force. Weight force. Boundary forces: plane constraints and tension of a rope. Static and dynamic equilibrium. Inclined plane. Gravitational friction forces: static friction and dynamic friction. Inclined plane with friction. Viscous friction force. Effect of air resistance on the fall of a body. Elastic force. Simple harmonic motion of a body attached to a spring. Forced harmonic motion and concept of resonance. Simple pendulum. Examples on ropes and pulleys.
3) WORK AND ENERGY.
Definition of work of a force. Examples of motor, null and resistant work. Power. Kinetic energy theorem. Kinetic energy. Examples of calculating work (weight force, elastic force). Conservative forces. Potential energy of elastic force and weight force. Mechanical energy. Conservation theorem of mechanical energy. Energy balance in the presence of nonconservative forces. Examples of energy analysis of motions: smooth inclined plane, inclined plane with sliding friction, mass attached to a spring, simple pendulum, "death lap." Relationship between potential energy and force. Qualitative analysis of motions from an energy point of view.
4) REFERENCE SYSTEMS AND RELATIVE MOTIONS.
Reference systems and relative motions. Transformations between reference systems. Law of composition of velocities and accelerations in relative motions. Inertial and non-inertial reference systems. Apparent or inertial forces. Examples of transformations between inertial and noninertial reference systems. Examples on apparent drag force. Apparent forces in rotating reference systems. Examples of motions in rotating reference systems: rotor of an amusement park, earth reference system.
5) SYSTEMS MECHANICS.
Introduction to systems mechanics. Center of mass. First cardinal equation of mechanics with examples. Principle of conservation of momentum. Angular momentum. Momentum of a force. Second cardinal equation of mechanics. Principle of conservation of angular momentum. Example: two masses rotating about their center of mass. Pairs of forces. Kinetic energy theorem and principle of conservation of energy for mechanical systems. Example: two masses disengaging from a spring. Resultant and resultant moment of weight force: center of mass. Center of mass reference system. König's theorems for angular momentum and kinetic energy. Bumps: general definitions, elastic shock (1D), inelastic shock (1D).
6) MECHANICS OF RIGID BODIES.
General definitions. Fundamental formula of rigid body kinematics. Translations and rotations. Angular momentum of a rigid body rotating about a fixed axis. Moment of inertia. Statics of the rigid body. Examples: swing, levers, ladder leaning against wall, balance of a body resting on horizontal plane. Examples of rigid body dynamics: compound pendulum, Atwood's machine with real pulley. Kinetic energy and work of internal forces in a rigid body. Example: Atwood's machine (pt. 2). Rolling and pure rolling motion of a rigid body. Example: wheel dragged by constant force on horizontal plane, wheel rolling on an inclined plane. Huygens-Steiner theorem. Continuous mass distributions. Example: calculation of moment of inertia of a linear mass distribution.
7) ELECTROSTATICS.
Introduction to electromagnetism. Electric charge and microscopic structure of matter. Electrostatics. Coulomb force. Electric field. Field lines. Continuous distributions of charge. Examples of electric field calculations from discrete charge distributions and continuous distributions (straight wire and uniformly charged ring). Flow of a vector field. Gauss' theorem: statement and meaning. Examples of application of Gauss's theorem: straight wire, uniformly charged sphere, uniformly charged plane. Potential energy and electrostatic potential. Example: uniformly charged double plane.
8) CONDUCTORS AND ELECTRICAL CURRENTS.
Conductors and insulators. Electrostatics of conductors. Electrostatic induction. Electrostatic shielding (Faraday cage). Capacitors. Capacitance of capacitor with flat and parallel faces, spherical capacitor, cylindrical capacitor. Capacitors and generators: energy analysis. Electrostatic energy in a capacitor. Capacitor systems in series and parallel. Examples of circuits with capacitors. Electric currents. Current intensity and electric current density. Ohm's law. Physical interpretation of Ohm's law. Ohm's second law. Joule effect. Electromotive force. Kirchoff's laws. Example: analysis of a circuit by Kirchoff's laws. Systems of resistors in series and parallel. RC circuit. Examples of circuits with generators and resistors.
9) MAGNETISM.
Magnetism. Hints at the magnetism of materials. Lorentz force and magnetic field. Motion of a charge in a uniform magnetic field. Laplace's second law. Example: forces acting on a current-carried coil. Magnetic field sources and Laplace's first law. Magnetic field generated by a circular coil and a straight wire run by current (Biot-Savart). Magnetic field lines. Ampere's theorem and its verification for a straight wire run by current. Example: magnetic field of a solenoid.
10) NON-STATIONARY ELECTROMAGNETIC PHENOMENA AND ELECTROMAGNETIC WAVES.
Maxwell's equations for nontime-dependent fields. Electromagnetic induction. Faraday-Lenz law. Examples: conducting track with sliding rod in magnetic field, alternator and alternating currents. Maxwell's equations for time-dependent fields. Introduction to electromagnetic waves. Wave equation. Monochromatic plane waves and fundamental quantities describing them. Energy of an electromagnetic wave. The electromagnetic spectrum.