28626 - General Physics T-A (L-Z)

Learning outcomes

After passing the final test, the student knows the general methodological aspects of physics (the important role of the experiments and the organization of the results in the framework of physics laws) and the fundamental concepts of the mechanics of the mass point and of the mass point systems. Moreover the student is able to apply these basic concepts to solve problems and examples.

Course contents

Requirements/Prior knowledge

A prior knowledge and understanding of basic mathematics is required to attend with profit this course: algebra, trigonometry, functions of one variable, derivatives, integrals, simple differential equations.

Fluent spoken and written Italian is a necessary pre-requisite: all lectures and tutorials, and all study material will be in Italian.

Course Contents

Introduction: Physics and the experimental method. The physical quantities and their measure process. Experimental errors. Main goals of the classical mechanics study. Units of measurement in physics. Systems of measurement, dimensions of a physical quantity, fundamental and derived physical quantities, the International System of Units (SI). Definition of reference frame.

Introduction to the vector calculus: Vector and scalar physical quantities. Vector definition and properties. Versor. Vector operations. Cartesian versors. Orthogonal Cartesian coordinate frame. Cartesian description of vectors. Vector operations in a Cartesian description. Polar coordinates in 2 and 3 dimensions (spherical and cylindrical). Versor derivative (Poisson formulae). Vector derivative. Partial derivatives. Nabla vector operator, gradient, divergence and curl in Cartesian coordinates. Definition of bound vector. Moment of a bound vector.

Kinematics (point mass): Definition of point mass, vector description of motion, “intrinsic” description of motion. Kinematics variables: position, velocity and acceleration vectors and their units. Motion classification. Uniform and uniformly accelerated linear motion. Motion of a falling body. Uniform and uniformly accelerated circular motion. Vector description of the circular motion and definition of the most relevant vector quantities. Angular velocity and acceleration. Connection between simple harmonic motion and uniform circular motion. Equation of the harmonic motion. Relative motion. Change of the reference frame. Transformation equations for position, velocity and acceleration. Galilean transformations.

Dynamics (point mass): Introduction. Force definition and units. Newton dynamics laws. Inertial reference frames. Momentum. Impuls of a force. Constraint forces. Weight. Dry friction, static and kinetic. Motion of a point mass on an inclined plane, with and without friction. Centripetal force: motion on a flat turn, on a banked turn with and without friction. Elastic force. Simple gravity pendulum. Conical pendulum with and without conical surface. Fluid friction. Work. Kinetic energy and theorem of the kinetic energy. Power. Work for weight, elastic force and friction. Potential energy. Potential energy, definition and evaluation for some forces. Conservative forces and properties. Force as gradient of the potential energy. Motion in a non-inertial reference frame. Fictitious forces. Definition of angular momentum and of torque. Theorem of the angular momentum. Central forces. Mechanical energy and angular momentum conservation in case of central forces.

Mechanics of point-mass systems: Definition of point-mass systems. Centre of mass and centre of gravity. Kinematical and dynamical variables for point-mass systems. Centre-of-mass theorems. Angular momentum theorem for a point-mass system. Dynamics equations for point-mass systems. Konig theorems: angular momentum and kinetic energy. Motion of the centre-of-mass and motion relative to the centre-of-mass. Centre-of-mass reference frame. Work for a point-mass system. Collisions and conservation laws of momentum, angular momentum, energy. Elastic and inelastic collisions.

Rigid body mechanics: Definition of rigid body. Fundamental equation of rigid body kinematics. Translation motion. Fixed axis rotation. Moment of inertia. Huygens–Steiner theorem. Rolling motion without slipping. Ballistic pendulum. Compound pendulum. Collision between a mass point and a rigid body and conservation laws. Fundamentals about static equilibrium for a rigid body.

Gravitation: Keler's law and universal gravitation law. Inertial and gravitational mass. Analogy between Moon and a falling body. Theorems of the shell. Motion of a mass point through an Earth tunnel. Gravitational constant G. Cavendish experiment an the measurement of the Earth mass. Gravitational potential energy and potenzial energy at the Earth surface. Escape velocity. Gravity close to the Earth surface: dependence of on the latitude and on the geoid.

Readings/Bibliography

• S. Focardi, I. Massa, A. Uguzzoni, M. Villa: Fisica Generale - Meccanica e Termodinamica, Casa Editrice Ambrosiana.

• P. Mazzoldi, M. Nigro, C. Voci: Fisica Vol.1 Meccanica - Termodinamica, EdiSES

• A. Bertin, S. De Castro, N. Semprini Cesari, A. Vitale, A. Zoccoli, Problemi di Esame di Fisica Generale, Società editrice Esculapio s.r.l. - Progetto Leonardo - Bologna.
• S. Rosati e R. Casali, Problemi di Fisica Generale (meccanica, termodinamica, teoria cinetica dei gas), Casa Editrice Ambrosiana.
• P. Pavan e F. Soramel, Problemi di Fisica risolti e commentati, Casa Editrice Ambrosiana.
• Any othe exercise-book available on the web or in a library.

Teaching methods

Traditional lectures, structured in theoretical parts, examples and exercises.

Assessment methods

The final exam aims at evaluating the level of acquired competence.

It is based on a written test, possibly completed by an optional oral exam.

In 2 and a half hours, students are required to answer 5 questions and to solve 3 to 5 exercises, without using books, notes and any other external help.

The minimum grade to pass the exam is 9 in answering questions + 9 in solving exercises.

The oral exam is optional and aims at increasing the grade of the written test or to confirm a higher than 26/30 grade. Only students successfully passing the written test can access the oral exam. In no case the oral exam can substitute a failed written test.

The oral test is a colloquium with the teacher, where the student shall show good knowledge of the course contents, understanding of the links between the different parts of the program and a proper scientific language.

Without oral exam a grade >26 will be decreased to 26/30. In order to get LODE, the student must get at least 29/30 in the written test and give an excellent oral exam, showing to have a perfect knowledge and understanding of the course topics.

More details on the exam rules can be found in the teacher's web site.

Students showing a good competence about the fundamental concepts of mechanics and adequate skills in solving the proposed problems can easily pass the exam. A higher grade is given to the students showing a full understanding of the course contents and advanced skills in solving complex problems.

A failing can be due to lack of knowledge or of understanding of the key concepts, to an insufficient thinking about these items and consequently to poor ability of problem solving.

Teaching tools

Lectures will be given at the blackboard. Occasionally slides and short movies can be used to facilitate the understanding of some concepts.

Office hours

See the website of Annarita Margiotta