# 27996 - General Physics T-1

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda. ## Learning outcomes

Basic concepts of classical mechanics and thermodinamics, with applications and exercises. Hits will be given to the limits of classical theory.

## Course contents

Vectors (6 hours). Physical quantities. Line segment. Directed line segment. Correspondence between points of the ordinary space and directed line segments. Equipollent directed line segments. Position vectors. Generic vectors. Free and bound vectors. Polar and axial vectors. Magnitude, direction and sense. Vector equality. Opposite vector and null vector. Vector addition and its properties. Vector subtraction. Triangle inequality. Scalar multiplication of a vector and its properties. Scalar products between two vectors and its properties. Square and magnitude of a vector. Versors (unit vectors). Scalar and vector component of a vector with respect to a direction. Magnitude of the sum of two vectors and of the difference between two vectors. Vector products between two vectors and its properties. Right-hand rule. Scalar triple product of three vectors.

Vector representations (6 hours). Orthogonal axis tern. Coordinate system. Cartesian, cylindrical, spherical and intrinsic coordinate systems. Versor bases. Cartesian, cylindrical, spherical and intrinsic (Frenet-Serret) versor bases. Relation between the versors of an orthonormal base. Line parametrisation. Arc-length parametrisation. Tangent versor. Osculating plane and osculating circle. Normal versor. Binormal versor. Curvature and torsion. Vector representation. Cartesian, cylindrical, spherical and intrinsic representation of the vectors. Representation of position vectors. Vector and vector representation. Active and passive transformations. Vector operations in the cartesian representation.

Rudiments of Vector Calculus (2 hours). Vectors dependent on a parameter and vector function of a variable. Vectors dependent on the point of application and vector fields. Derivative and primitive function of a vector function of a variable. Derivatives of the versors of a base with respect to the coordinates: cartesian, cylindrical and intrinsic base. Frenet-Serret formulas. Differential displacement vector in cartesian, cylindrical, spherical and intrinsic base. Differential volumes and areas in cartesian, cylindrical, spherical and intrinsic base. Differential operators. The nabla (del) symbol. Gradient of a scalar field. Divergence and curl of a vector field.

Particle Kinematics (8 hours). Point particle, systems of point particles and rigid bodies. Reference frames and Cartesian coordinate triads. The principle of special relativity. Time intervals and their measurement. Short history of the time unit. Solar and sidereal day. length and its measurement, Short history of the length unit. The vector law of motion in a cartesian, cylindrical, spherical and intrinsic base. Average and instantaneous velocity. Instantaneous velocity in a cartesian, cylindrical and intrinsic base. Average and instantaneous speed. Limits to the concept of instantaneous velocity: the instantaneous velocity of a free electron. Instantaneous areal velocity. Vector expression of instantaneous areal velocity. Expression of the instantaneous areal velocity in the cylindrical base. Average and instantaneous acceleration. Instantaneous acceleration in a cartesian, cylindrical and intrinsic base. Magnitude of the acceleration vector.

Relative motion (2 hours). Change of reference frames. Translation and rotation. Transformation of the position vector. Constant vectors in a given reference frame. Transformation of the time derivative of a vector. Angular velocity. Poisson’s formula. Poisson derivation rule. Transformation of the velocity. Drag velocity. Transformation of the acceleration. Drag acceleration and Coriolis acceleration.

Rigid body kinematics (1 hour). Constraints and degrees of freedom. Kinematics of the rigid bodies. Fundamental formula of the kinematics of the rigid bodies. Translational motion, rotative motion. Pure rolling.

Applied Vectors (2 hours). Polar and axial moment of an applied vector. Resultant, resultant moment and axial resultant moment of an applied vector system. Centre of parallel vectors. Equivalent systems of applied vectors. Couple of applied vectors. Reduction of an applied vector system to a vector and a couple.

Statics (2 hours). Force. Dynamometer. The vector nature of a force. Force units in International System of Units. Weight-force. Centre of gravity (or barycentre) and its properties. Elastic force and Hooke’s law. Internal and external forces. Cardinal equations of statics (equilibrium equations). Calibration of a Dynamometer. Active and constraint forces. Friction forces. Sliding friction. Static and kinetic sliding friction. Limiting friction. Rolling friction

Particle Dynamics (6 hours). Dynamics and its principles. Frame of reference. Particle subject to null net force. Inertial and non-inertial reference frames. The Newton’s first law of motion (law of inertia). Approximatively inertial reference frame. The physics origin of the inertiality. Mach’s principle and strong equivalence principle. Free falling reference frames. Historical note on the first principle. Motion in pre-Galilean natural philosophy. The classic statement of the first law of motion and its limits. The Newton’s second law of motion. Dynamic measure of the force. Short story of the mass units. Weight units and dynamics. Density. Units of measurement and dimensional analysis. Mass and weight. Momentum and impulse. Impulse-momentum theorem. Kepler's laws. Newton's law of universal gravitation: force direction, dependence of gravitational force on mass and distance, universality. Central forces. Cavendish experiment. Inertial mass and gravitational mass. Forces depending on position, velocity and time. Implicit and explicit time dependence. Fundamental particle dynamics problem.

Remarkable exercises on motions (3 hours). Uniformly accelerated rectilinear motion. Free fall in the gravitational field of a body in vacuum. Motion of a projectile in vacuum. Range and highest trajectory point. Motion of a body in a viscous fluid. Linear drag and quadratic drag. Drag coefficient. Motion of a sphere with linear drag. Free fall in the gravitational field of a sphere with linear drag. Terminal velocity. Motion of a sphere with quadratic drag. Free fall in the gravitational field of a sphere with quadratic drag. Motion of a sphere thrown upward in the gravitational field with quadratic drag. Simple harmonic oscillator. Simple harmonic motion: period, frequency and angular frequency. Simple pendulum: solution of the motion equation for small oscillation amplitudes. Damped oscillator. Over-damped, critically damped and under-damped motion. Driven oscillator. Transient state and steady state. Resonance.

Pseudo-forces (5 hours). Motion in a non-inertial reference frame. Acceleration of a particle subject to null net force. Pseudo-forces. Examples of pseudo-forces. Change of reference frame. Rectilinear uniform translating reference frame. Accelerated reference frame. Drag pseudo-force and Coriolis pseudo-force. Centrifugal pseudo-force and Euler pseudo-force. Telling the pseudo-forces from the real forces. Examples. Pseudo-forces effect in Earth frame. 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. Dependency of the rotation speed of the swing plane on the latitude.

Dynamics of particle systems and of rigid bodies (5 hours). Action-reaction law. Resultant and resultant moment of internal forces. Closed systems. Angular momentum. Cardinal equations of dynamics. Conservation of momentum and of angular momentum. Centre of mass. Centre of mass and centre of gravity. Properties of the centre of mass. The centre of mass theorem. Consequences of the cardinal equations of dynamics on planet motion. Angular momentum of rigid bodies: case of a rigid body rotating around a fixed axis and case of a roto-translating rigid body with the rotation axis parallel to itself. Moment of inertia. Moment of inertia of homogeneous bodies. Huygens [http://en.wikipedia.org/wiki/Christiaan_Huygens] –Steiner [http://en.wikipedia.org/wiki/Jakob_Steiner] theorem. Dynamics of systems.

Work and energy (5 hours). Elementary work. Exact differentials and differential forms. Line integral of a vector field. Surface integral of a vector field. Work done by a force on a point particle moving on a curve. Examples of work calculation. Kinetic energy. The work-energy theorem. König's theorem for a system of particle points and for a rigid body. The work of the weight-force. Positional forces and conservative forces. Differential operators: gradient, divergence and curl. Physical meaning of the curl. Stoke’s theorem. Properties of conservative force fields. Potential, potential energy and total mechanical energy. Conservation of mechanical energy. Collisions. Collision forces. Elastic and inelastic collisions. Conservation of mechanical energy, linear momentum and angular momentum in collisions processes between rigid bodies.

Recapitulation Exercises on Mechanics (7 hours).

Thermodynamic systems and molecular motions (10 hours). Extension of the principle of energy conservation to dissipative forces: internal energy. Kinetic molecular theories. Relations between macroscopic thermodynamic quantities and microscopic mechanical quantities. Microscopic mechanical reversibility and macroscopic thermodynamic irreversibility. Free expansion of a gas and spontaneous compression: Poincaré's time. Intensive and extensive quantities. Thermodynamical equilibrium. Adiabatic and diathermic walls. Thermal contact. Thermal equilibrium between two thermodynamical systems. Thermometers: thermometric materials, thermometric properties and thermometric functions. Zeroth law of thermodynamics. Thermometer calibration. Fixed points: normal melting point, normal boiling point and triple point. Ideal gas thermometer. Units of measurement of the temperature. International temperature scale. Thermodynamic transformations. Quasi-statics thermodynamic processes. Clapeyron diagram. Adiabatic quasi-statics thermodynamic processes of a gas. Quasi-statics isochoric heating and cooling of a gas. Equation of state of an ideal gas. Mole and Avogadro’s number. Atomic mass and molecular mass: the unified atomic mass unit. Isothermal processes of real fluids. Critical temperature. Saturated vapor pressure. Changes of the aggregation state. Van der Waals equation: co-volume and internal pressure constant. Ebullition. Bubble chambers.

First principle of the thermodynamics (6 hours). Average molecular kinetic energy. The work in a quasi-static transformations of a fluid. Adiabatic work. Internal energy. Amount of heat. The first principle of the thermodynamics. Heat capacity, specific heat and molar heat. Latent heats. Ideal gases. Technical work and enthalpy. Property of ideal gases. Quasi-static adiabatic transformations of an ideal gas: Poisson's formulae.

Second principle of the thermodynamics (10 hours). Reversible and irreversible transformations. Heat engines. Efficiency of a heat engine. Carnot's cycle. Refrigerating systems. Second principle of the thermodynamics: Kelvin-Planck and Clausius statements and their equivalence. 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. Example of calculations of entropy variation in a reversible or irreversible thermodynamic process. 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.

Recapitulation Exercises on Thermodynamics (4 hours).

## Readings/Bibliography

• Copy of the transparencies presented during the course, available on World Wide Web at the web site Insegnamenti OnLine: https://iol.unibo.it/ .
• Question and exercises for the assessment, available on World Wide Web at the at the web site Insegnamenti OnLine: https://iol.unibo.it/ .
• Basic textbook in Italian language (alternatively):
• Bertin, Poli, Vitale, Fondamenti di Meccanica, Progetto Leonardo, Esculapio, Bologna, ISBN-10: 8886524048, ISBN-13: 978-8886524049 + Bertin, Poli, Vitale, Fondamenti di Termodinamica, Progetto Leonardo, Esculapio, Bologna, ISBN-10: 8886524153, ISBN-13: 978-8886524155.
• Mencuccini, Silvestrini, Fisica. Meccanica e termodinamica, Casa Editrice Ambrosiana, ISBN-10: 8808186490, ISBN-13: 978-8808186492.
• Focardi, Massa, Uguzzoni, Villa, Fisica Generale, Meccanica e Termodinamica, Casa Editrice Ambrosiana, Milano, ISBN-10: 8808182150, ISBN-13: 978-8808182159.
• Basic textbook in English language (alternatively):
• Hugh D. Young, Roger A. Freedman, University Physics with Modern Physics, Volume 1, (14th Edition), Pearson, ISBN-10: 0133978044, ISBN-13: 978-0133978049.
• Douglas C. Giancoli, Physics for Scientists & Engineers, Vol. 1, Pearson, ISBN-10: 0132273586, ISBN-13: 978-0132273589.
• David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, Volume 1, (10th edition), Wiley, ISBN-10: 111823376X, ISBN-13: 978-1118233764.
• Randall D. Knight, Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition), Pearson, ISBN-10: 0133942651, ISBN-13: 978-0133942651.
• Books for knowledge improvement in Italian language:
• Feynmann, La fisica di Feynmann, volume 1 - Meccanica, radiazione, calore, Zanichelli, Bologna, ISBN: 9788808478153.
• Books for knowledge improvement in English language:
• Feynmann, The Feynman Lectures on Physics, volume 1 - Mainly Mechanics, Radiation, and Heat, Addison Wesley, ISBN-10: 0201021161, ISBN-13: 978-0201021165.
• Books of exercises:
• Longhi, Nisoli, Osellame, Stagira, Fisica sperimentale. Problemi di meccanica e termodinamica, Esculapio editore, ISBN-10: 8874880588, ISBN-13: 978-8874880584.
• Poli, Esercitazioni di Fisica 1, Pitagora editore, ISBN-10: 883710023X, ISBN-13: 978-8837100230.

## Teaching methods

• The course is based on lectures dealing with the theoretical aspects of the programme topics and application exercises.
• Lectures make use of both blackboard and projector.
• The slides presented at the lectures are made available to the students before the lecture by means of the World Wide Web, at the site Insegnamenti OnLine: https://iol.unibo.it/, in order to reduce the time and the work of mere transcription during the lectures.
• The attendance at the lectures is not compulsory, however, in facts, it is needful for achieving the expected learning outcome in the foreseen time.
• The proposed practices demand the use of the pocket calculator.
• Concerning Module 1:
• Lecturer-student communication about the course topics and organisation make use of the fora available on the web site Insegnamenti OnLine: https://iol.unibo.it/ .
• The lecturer makes use of questionnaires, available on the web site Insegnamenti OnLine: https://iol.unibo.it/, in order to gather students’ feedback on the understanding on the programme topics.

## Assessment methods

• Concerning Module 1:
• The assessment is based, for 3/30 on the homework assignments and for 28/30 on the final exam.
• The final examination can be hold face-to-face or remotely (depending on the state of the COVID-19 infection).
• In both the cases the examination is written and consists in 2 parts.
• The first part consists of questions concerning the topics introduced during the lectures, with the aim of verifying that the student has deeply understood the physics principles and is able to apply them in formulating the laws which regulate specific physical phenomena; the students are required to select an answer between a multiple choice or to write concise open answers; in the latter case, the assessment is based on accuracy, completeness, clearness and conciseness (in decreasing weight order).
• The second part consists of exercises relating to the topics introduced during the lectures, aimed to verify that the student is able to deal with real problems by using the physics principles and laws, in order to get the numerical values of the requested physical quantities, expressed in the proposed units, thus revealing experience in dimensional analysis and ability to execute calculations with the required approximation; the assessment is based on the accuracy of the numerical results.
• The pass of the exam requires a good rating in both the parts (question and exercises).
• In case of exam pass, the grade is the mean value between the grades of the two parts (questions and exercises), rounded to the nearest integer.
• Full marks with distinction (laude) is attributed to an exam grade only if both exam parts (question and exercises) show an excellent skill of the student.
• All the assessments greater than 23/30 have to be confirmed by an oral exam.
• Further details are available in the web site Virtuale: https://virtuale.unibo.it/.
• Concerning Module 2:
• The examination is written and consists in 1-2 exercises and 2 question concerning theory.
• The pass of the exam requires a good rating (18/30) in both the modules.
• In case of exam pass, the grade is the mean value (weighted by the credit numbers) between the grades of the two modules, rounded to the nearest integer.
• Full marks with distinction (laude) is attributed to an exam grade only if both modules show an excellent skill of the student.

## Teaching tools

• Slides presented at the lectures, available to the students before the lecture by means of the World Wide Web, at the site Insegnamenti OnLine: https://iol.unibo.it/ . Student should print the slides and take them to the lecture, in order to write on them additional notes.
• Concerning Module 1:
• List of exam exercises and questions, available to the students by means of the World Wide Web, at the site Insegnamenti OnLine: https://iol.unibo.it/ .
• Fora available on the web site Insegnamenti OnLine: https://iol.unibo.it/, for lecturer-student communication about the course topics, discussion, and requests of enlightenment.
• Anonymous questionnaires, available on the web site Insegnamenti OnLine: https://iol.unibo.it/, to gather students’ feedback on the understanding on the programme topics.

## Links to further information

https://virtuale.unibo.it/course/view.php?id=17671

## Office hours

See the website of Domenico Galli

See the website of Silvia Castellaro