16726 - General Physics A

Course contents

1. Rudiments of vector calculus . Vectors, unit vectors and vector components. Operations on vectors. Cartesian representation of the vectors. Polar moment and axial moment of a vector. Resultant and resultant moment. Equivalent sets of applied vectors. Pairs of vectors.
2. Kinematics. Reference frames and Cartesian coordinate systems. The principle of relativity. Intrinsic description and Cartesian description of the motion. Intrinsic, Cartesian and cylindrical expression of the velocity and of the acceleration. Areal velocity. Constraints and degrees of freedom. Kinematics of the rigid bodies. Poisson formulae. Fundamental formula of the kinematics of the rigid bodies. Translational motion, rotative motion, pure rolling, angular velocity. Change of reference frames. Galileo's transformations. Transformation of the velocity and of the acceleration.
3. Statics. Static measurement of the forces. The cardinal equations of statics. Centre of gravity. Constraints and constraint forces. Friction between solid bodies. Static and dynamic friction. Sliding and rolling friction.
4. Particle Dynamics. Inertial reference frames. First and second principle of dynamics. Mass and density. Mass and weight force. Momentum and impulse. Theorem of the impulse. Kepler's laws and Newton universal law of gravitation. Cavendish experiment. Inertial mass and gravitational mass. Motion of a body in a viscous fluid: laminar and turbulent flow, Reynolds number, drag coefficient, viscous resistance and hydraulic resistance. Fall of body in presence of viscous drag or hydraulic resistance. Harmonic oscillator, damped oscillator, forced oscillator, resonance. Small oscillations of a simple pendulum.
5. Numerical solution of the fundamental problem of the particle dynamics . Notes on the Euler-Cauchy and the II order Runge-Kutta methods. Graphical interpretation of the Euler-Cauchy and the II and IV order Runge-Kutta methods. Implementation of the Euler-Cauchy and of the II and IV order Runge-Kutta algorithms in the C and Java languages. Motion in presence of viscous drag and hydraulic resistance. Fall of a body in presence of viscous drag and hydraulic resistance. Harmonic oscillator, damped oscillator, forced oscillator, interference between the transitory and the stationary solution of the forced oscillator, transitory beats. Simple pendulum.
6. Inertial forces. Reference frames in accelerated translational and rotative motion with respect to the fixed stars. Drag force, centrifugal force and Coriolis force. Dependency of the weight force on the latitude. Deviation towards east of the free falling bodies. Deviation of the bodies in motion on the Earth surface. Foucault pendulum.
7. Dynamics of particle systems and of rigid bodies. Third principle of dynamics. Internal and external forces. Isolated systems. Cardinal equations of dynamics. Centre of mass and centre of gravity. Angular momentum of the rigid bodies. Moment of inertia, Huygens-Steiner's theorem.
8. Work and energy. Work. The work-energy theorem. Kinetic energy. König's theorem. Conservative force fields their properties. Potential and potential energy. Principle of conservation of the mechanical energy. Collision forces. Elastic and inelastic collisions.
9. Thermodynamic systems and molecular motions. Molecular motions in solid bodies and gases. Microscopic mechanical reversibility and macrocospic thermodynamic irreversibility. Free expansion and spontaneous compression: Poincaré's time. States of aggregation of the matter. Thermodynamic equilibrium. Temperature and its measure. Zero principle of the thermodynamics. Thermodynamic transformations. The ideal-gas law. Isotherm transformations of real fluids. Changes of the aggregation state. Saturated vapour pressure. Ebullition. The real-gas laws. The equation of state of Van der Waals. First principle of the thermodynamics.
10. First principle of the thermodynamics. The work in a quasi-static transformations of a fluid. The first principle of the thermodynamics. Internal energy. Amount of heat. Heat capacity, specific heat and molar heat. Latent heats. Technical work and enthalpy. Property of ideal gases. Quasi-static adiabatic transformations of an ideal gas, Poisson's formulae.
11. Second principle of the thermodynamics. Reversible and irreversible transformations. Heat engines, efficiency. Carnot's cycle. Refrigerating systems. Second principle of the thermodynamics. Impossibility of the perpetual motion of first and second species. The Carnot's theorem. Absolute thermodynamic temperature. The Clausius's theorem. Entropy. The law of the increase of the entropy. The equation of the internal energy. The equation of the enthalpy. The equations of the TdS. Helmholtz and Gibbs's thermodynamic potentials and their properties.

Readings/Bibliography

• Copy of the transparencies presented during the course, available on World Wide Web at the URL: https://lhcbweb.bo.infn.it/twiki/bin/view.cgi/GalliDidattica/GalliTrasparenze.
• Question and exercises for the assessment, available on World Wide Web at the URL: https://lhcbweb.bo.infn.it/twiki/bin/view.cgi/GalliDidattica/GalliDomandeEsercizi.
• Java applet for the numerical solution of problems of Physics, available on World Wide Web at the URL: http://ishtar.df.unibo.it/Uni/bo/ingegneria/all/galli/stuff/fisicaInterattiva/index.html.
• Halliday, Resnick, Krane, Physics, vol. 1, John Wiley & sons.
• Feynmann, Leighton, Sands, The Feynmann Lectures on Physics, vol I, Addison-Wesley.
• Bertin, Poli, Vitale, Fondamenti di Meccanica, Progetto Leonardo, Esculapio, Bologna.
• Bertin, Poli, Vitale, Fondamenti di Termodinamica, Progetto Leonardo, Esculapio, Bologna.
• Rosati, Casali, Problemi di Fisica Generale, volume 1, meccanica, termodinamica, teoria cinetica dei gas, seconda edizione, Casa Editrice Ambrosiana, Milano.
• Salandin, Pavan, Problemi di Fisica risolti e commentati, volume 1, Casa Editrice Ambrosiana, Milano.

Teaching methods

• During the frontal lessons slides are shown by means of a projector connected to a PC.
• Such transparencies are made available to the students before the lesson by means of World Wide Web, in compact format (4 slides for page) and printable, in order to reduce the time and the work of mere transcription during the lessons.
• The proposed practices demand the use of the pocket calculator.
• The course is integrated by practices on a PC, executables either in the classroom or individually in the laboratory of computer science or at home. The teacher makes available to the students, on the World Wide Web, a series of Java Applets for the solution of physics problems, both in executable format (executable in any Java 2 compatible web browser) and in the source code (modifiable by the students). Such didactic material can be used in different ways.
• A first type of use simply consists in executing the programs many times over, modifying the problem parameters and the initial conditions from time to time, in order to interactively study the dependency of the solutions of the physical problems on the parameters and the initial conditions.
• A second level of use consists in analyzing the calculation program in order to understand how the physical problem can be formulated in order to be solved by means of numerical calculation.
• A third level of use consists in comparing the numerical solutions with the analytic solutions (for problems in which both solutions are possible) in order to interactively understand the errors introduced by the approximations used in the numerical calculation and their dependency on the parameters of the calculation.

Assessment methods

• The examination consists of a written test.
• Tests are constituted by at least 3 problems to resolve and at least 4 questions to answer.
• The assigned maximum time for the written tests is 90 minutes.
• Exercises are randomly chosen by a list of a few hundreds of exercises, available to the students through the World Wide Web (the last version available on the Web 15 days before the test is used). Their evaluation is based on their numerical results, which depend on a number randomly assigned to the students. The single exercise evaluation is 3/3 if the result is correct within 5 units of the third significant digit, is 2/3 if the result is correct within 10 units of the third significant digit, is 1/3 if the result is correct within 20 units of the third significant digit or if the mantissa of the result is correct within 5 units of the third significant digit but the exponent differs by one unit. In any other case the evaluation is 0/3.
• The questions are randomly chosen by a list of a few hundreds of questions, available to the students through the World Wide Web (the last version available on the Web 15 days before the test is used). To each question is assigned a rating in the range 0-3.
• In order to participate to the written tests it is necessary to enroll itself in the lists available on the UNIWEX system at least eight days early with respect to the date of the examination.
• The exam of General Physics (C.I.) is passed if the average of the evaluation of the part A and B is greater than or equal to 18/30 and if the single evaluation is greater than or equal to 15/30.
  

Teaching tools

Projector, PC.

Links to further information

https://lhcbweb.bo.infn.it/GalliDidattica

Office hours

See the website of Domenico Galli