Chemical Sciences

The course is made of two separate units: Mechanics (60 hours) and Statistics (30 hours). Mechanics Introduction to the scientific method: - Physical quantities and their operational definition - Concept of units of measurement and dimensional equations - Systems of units of measurement and fundamental quantities - The International System (IS) Kinematics of the material point: - Kinematic equations of motion, speed, acceleration - Rectilinear motions (uniform, uniformly accelerated), harmonic motion, circular motion, parabolic motion. Dynamics of the material point: - Principle of inertia and introduction to the concept of force - Newton's second law and principle of action and reaction - Momentum and impulse of a force - Resultant of forces, static equilibrium and dynamic equilibrium - Bond reactions and wire tension - Sliding friction force (static, dynamic) and viscous - Elastic force - Work of a force, power and kinetic energy - Conservative forces and potential energy - Mechanical energy and its conservation - Angular momentum and moment of force Relative motions: - Reference systems and generic relative motion - Inertial reference systems Dynamics of material point systems: - Center of mass of a system and motion of the center of mass - Momentum and its conservation - Angular momentum theorem - Center of mass reference system - König's theorems - Collisions (elastic, inelastic) Rigid body dynamics: - Definition and properties of the rigid body - Rigid body motions, rotations around an axis - Moment of inertia and Huygens-Steiner theorem Statistics Introduction to uncertainty analysis: - Definition and importance of uncertainties - Representation and significant figures - Comparison between measurements and discrepancies - Verification of relationships between quantities using graphs Propagation of uncertainties: - Sums and differences - Products and quotients Random uncertainties: - Random and systematic errors - Mean and standard deviation Statistical distributions: - Normal distribution - Poisson distribution - Binomial distribution Data analysis: - Least squares method - Covariance and correlation - Chi-square test

Knowledge of basic algebra and trigonometry, understanding of differential and integral calculus in one variable, graphical representation of functions.

Mechanics: P. Mazzoldi, M. Nigro, C. Voci, Elementi di Fisica (Meccanica e Termodinamica), EdiSES, III edizione. Statistics: John R. Taylor, Introduzione all'Analisi degli Errori (lo studio delle incertezze nelle misure fisiche), Zanichelli, II edizione.

The final assessment is based on a written exam and an oral exam. The written exam will consist of one or more exercises on the topics covered in class and during the exercises. During the course of the lessons, there will be two interim tests, which can replace the final written exam. The interim tests will be reserved for those actively participating in the course, regardless of their year of study.

Mechanics: P. Mazzoldi, M. Nigro, C. Voci, Elementi di Fisica (Meccanica e Termodinamica), EdiSES, III edizione. C. Mencuccini, V. Silvestrini, Fisica 1. Meccanica e termodinamica, Liguori Editore. M. Zani, L. Duò, P. Taroni, Esercizi di Fisica (Meccanica e Termodinamica), EdiSES. Statistics: John R. Taylor, Introduzione all'Analisi degli Errori (lo studio delle incertezze nelle misure fisiche), Zanichelli, II edizione. G. Filatrella, P. Romano, Elaborazione statistica dei dati sperimentali, EdiSES, II edizione.

The course involves only in-person classes, with approximately one-third of the teaching hours dedicated to problem-solving in preparation for the final written exam.

Mechanics: The scientific experimental method. Physical quantities and units of measurement. Position, speed and acceleration. Frames of reference in relative motion. Inertial reference systems. Principle of inertia. Force, inertial mass and gravitational mass. Second law of motion. Third law of motion. Non-inertial references, apparent forces. Static friction. Dynamic friction. Elastic forces. Impulse and momentum. Moment of force and angular momentum. Pendulum. Work of a force. Kinetic energy theorem. Conservative fields. Potential energy. Conservation of mechanical energy. Equilibrium of a particle. Harmonic oscillator. Momentum and total angular momentum for a system of particles. Center of mass. Center of Mass reference frame. Cardinal equations. Two-body problem. Koenig’ Theorem. Elastic and inelastic collisions. Rigid systems. Moment of inertia. Longitudinal and transverse elastic waves. Wave equation. Sine waves. Interference. Standing waves. Laboratory of Physics I: The experimental method; Introduction to measuring uncertainty; Calculation and representation of error; Error propagation; Statistical analysis of casual uncertainty; Statistical distributions; The Normal distribution; The least square method; The chi-square method.

Basic Knowledge of the fundamentals of probability and of differential and integral calculus. -Trigonometry

Mechanics: P.P. Mazzoldi, M. Nigro, C. Voci (MNV) Elementi di Fisica, Meccanica e Termodinamica Edises, III edizione, ISBN 978-88-36-23036-5 Statistics and data analysis: J. R. Taylor (JRT) Introduzione all'analisi degli errori, Lo studio delle incertezze nelle misure fisiche Zanichelli, III edizione, ISBN 978-88-08-39966-3 Exercises: E. Placidi (EP) Esercizi di Meccanica e Analisi degli errori Edises, ISBN 978-88-36-23168-3 E. Milani, M. Marinelli, G. Verona Rinati, C. Verona Meccanica e termodinamica Guida alla Soluzione degli Esercizi da Mazzoldi, Nigro, Voci - Fisica Mazzoldi, Nigro, Voci - Elementi di Fisica, Edises, ISBN 978-88-36-23167-6.

Attendance is optional although strongly recommended.

There is a written exam and an oral exam. Passing the written exam (grade >17) is mandatory in order to take the oral exam. The evaluation of the written exam takes into account the answers to the questions in the form of implicit equations as well as in terms of numerical results, with the appropriate units. In addition to the correctness of the procedure identified to solve the question, the adequacy of the proposed solution is also evaluated in relation to the skills that the student is expected to have acquired at the end of the course. The explanation of the solution is expected to be provided using an appropriate language. The written exam can be replaced by ongoing tests (esoneri) on reduced parts of the syllabus. The written exam usually lasts two hours, with two exercises on different topics of the course, while the tests (esoneri) last one hour and half, with one exercise. In the oral exam evaluation, the following aspects are taken into account: the general preparation of the student, which must cover the entire syllabus, the reasoning skills and the explanatory accuracy. The oral exam lasts 45-60 minutes per student. In the overall evaluation of the exam and for the determination of the final grade, the written and the oral exams have equal weight, i.e. 50% each.

The course is divided into lectures and classroom exercises. Classroom lessons are integrated with eLearning and Google Classroom material The course consists of about 90 hours of teaching (2/3 mechanics-1/3 statistics and data analysis) of which 1/3 of classroom exercisesThe lectures provide the basis to understand the theory part which will need to be studied in greater detail using the textbooks. The classroom exercises allow the students to acquire the basic concepts and the strategy needed to solve mechanics problems. They also provide more insights about the theoretical part of the course. The main goal of these classes is to let the student pass the written exam

Introduction to the scientific method: physical quantities, dimensional analysis, units of measurement (international system, SI). Kinematics: velocity, acceleration, uniform rectilinear motion, uniformly accelerated motion, grave motion, circular motion. Dynamics: first, second and third principles of dynamics, friction force, gravity force, constraint reactions, elastic force and harmonic motion. Work and Energy: work of a force, kinetic energy theorem, conservative forces, potential energy, conservation of mechanical energy. The free and forced harmonic oscillator. The resonance. Outline of error analysis. Classical mechanics of systems of material points Dynamics of a system of material points: momentum, first cardinal equation, conservation of momentum, the center of mass theorem, the momentum of a force, collisions (elastic, anelastic, and completely anelastic), kinetic energy theorem for a system of material points. Rigid body dynamics: force momentum, equilibrium conditions of the rigid body, angular momentum, second cardinal equation, conservation of angular momentum, rotational motions of the rigid body. Physics Laboratory I: The experimental method; General notions on measurement uncertainty; Determination and representation of the error; Uncertainty propagation; Statistical analysis of random uncertainties; Statistical distributions (Poisson, Binomial); The normal distribution; minimum square method; The test chi-square for a distribution; Covariance and Correlation; Central limit theorem.

Knowledge of algebra; trigonometry; basics of differential and integral calculus including derivatives, integrals, and series development of elementary functions; graphical representation of functions.

P. Mazzoldi, M. Nigro, C. Voci (MNV) Elementi di Fisica Edises, III edizione, ISBN 978-88-3623-036-5 Esercizi: E. Placidi Esercizi di Meccanica e Analisi degli errori: Ernesto Placidi, ISBN: 978-8836231683 Ed. Edises (2023) John R. Taylor, Introduzione all'analisi degli Errori, seconda edizione (Zanichelli).

The course is divided into lectures and classroom exercises. Classroom lessons are integrated with eLearning and Google Classroom material (course code cxcgz2b)

Attendance is optional although strongly recommended.

Student evaluation is based on a written test and an oral interview. Those who pass the two ongoing written tests that take place during the course are exempt from the written test. The written test and the exemptions are composed of physics exercises based on the course program. The weight of the oral exam is about 60% of the total evaluation, while 40% is linked to the written test. Dates of the exams: 16/06/2023 17/07/2023 12/09/2023 08/11/2023

C. Mencuccini, V. Silvestrini (MS) Meccanica e Termodinamica Casa Editrice Ambrosiana, I edizione, ISBN 978-88-08-18649-2 R. A. Serway, J. W. Jewett Jr., Fisica per Scienze ed Ingegneria - Vol. I - Meccanica e termodinamica, Ed. Edises Universitaria L. Duò, P. Taroni, Fisica Meccanica e Termodinamica, Edises, ISBN 978-88-36-23028-0 Exercises books: Esercizi di meccanica: Loreto, Baldassarri, Servedio, Tria - "Fisica Generale (Meccanica)", Ed. McGraw-Hill Esercizi di meccanica e termodinamica (capitolo 1-8 + appendice A): Alippi, Bettucci, Germano - "Fisica Generale", Società Editrice Esculapio Esercizi di meccanica e termodinamica: Mencuccini, Silvestrini - "Esercizi di Fisica Meccanica e Termodinamica" , Casa Editrice Ambrosiana

The course is divided into lectures and classroom exercises. Classroom lessons are integrated with eLearning and Google Classroom material (course code cxcgz2b)