Learning objectives
The objectives of the Course are:
- to provide a conceptual understanding of the fundamental laws of classical Mechanics, including systems dynamics, and of Thermodynamics, with particular focus on kinematics, Newton’s laws and conservation principles;
- to develop some understanding of main aspects of the dynamics of rigid bodies and of gravitation;
- to treat the mechanics of continuum systems (fluids and elastic properties of solids), the thermology and the thermodynamics from a phenomenological viewpoint;
- to initiate the description of oscillatory and wave phenomena.
The aim of the course is, from one hand, to give the analytical instruments that allows describing the dynamics of the most simple mechanical and thermodynamic systems and examining their qualitative behaviour, even through the development of problem solving skill. On the other hand the course will provide the conceptual basis of the newtonian formulation of Mechanics, which is preparatory to the formalizations described in more advanced courses.
Prerequisites
- Working knowledge of high school level algebra and trigonometry;
- Differential and integral calculus
- Principles of analytical geometry and of elementary vector analysis
Course unit content
Part I
1. Mechanics: introduction
2. Kinematics of Material Point
3. Dynamics of material point: Force and Newton’s laws
4. Applications of Newton’s laws
5. Work and mechanical Energy
6. Dynamics of the systems of material points
7. Dynamics of the rigid body I: moment of inertia and Newton’s 2nd law
Part II
8. Dynamics of the rigid body II: angular momentum, statics
9. Energy conservation
10. Collisions
11. Gravitation: phenomenology and Newton’s law
12. Elastic properties of solids
13. Fluid statics
14. Fluid dynamics
15. Oscillatory phenomena
Part III
16. Wave phenomena: elastic waves
17. Thermodynamic systems and Thermology
18. Ideal and real gases
19. Heat and first law of thermodynamics
20. Applications of the first law of thermodynamics
21. Second law of thermodynamics
22. Entropy
Full programme
Part I
1. Mechanics: introduction
Classical Mechanics and Thermodynamics; Physics and measurements; physical quantities and units. Elements of vector algebra: general properties of vectors; unit vectors; vector components; dot product and cross product; rectangular coordinates in 2-D and 3-D; vector derivatives.
2. Kinematics of Material Point
Material Point scheme. Position, velocity, acceleration vectors: constant-velocity and constant-acceleration motion. Free body fall. Planar motions: projectile motion; circular motion; centripetal acceleration; angular Kinematics. Simple harmonic motion.
3. Dynamics of material point: Force and Newton’s laws
Interactions, the conception of force; Newton’s laws; inertial reference systems; mass and weight; linear momentum and its conservation, general form of the Newton’s 2nd law; impulse and impulse theorem.
4. Applications of Newton’s laws
Contact forces: tension, normal force; forces of static and dynamic friction; elastic force and Hooke’s law. Dynamics of the uniform circular motion: centripetal force. Simple pendulum and conical pendulum. Inertial frames of reference: galileian relativity. Non-inertial frames of reference, fictitious forces. Rotating frames of reference: Coriolis’ force. The earth frame of reference.
5. Work and mechanical Energy
Work of a constant and of a variable force; work-energy theorem for a particle. Power. Conservative and non-conservative forces; potential energy: elastic, gravitational; mechanical energy and its conservation in isolated conservative systems; general treatment of one-dimensional and three-dimensional conservative systems.
6. Dynamics of the systems of material points
Motion of a system of particles; centre of mass and its motion; Newton’s 2nd law for a system of particles; conservation of linear momentum; centre of mass reference system; work-energy theorem.
7. Dynamics of the rigid body I: moment of inertia and Newton’s 2nd law
Rigid body scheme, density, centre of mass; translation, rotation and roto-translation; torque and moment of force; moment of inertia; Newton’s 2nd law for rotational motions; Huygens-Steiner theorem; centre of gravity. Rolling motion of rigid bodies. Work and kinetic energy in the rotational and roto-translational motions.
Part II
8. Dynamics of the rigid body II: angular momentum, statics
Angular momentum of a particle, of a system of particles and of a rigid body; theorem of angular momentum; symmetry of bodies; angular momentum and frames of reference; angular momentum conservation. Static equilibrium of a rigid body.
9. Energy conservation
Generalization of the principle of conservation of mechanical energy; work of external forces; internal energy for a system of particles; energy conservation for a system of particles; energy associated to the centre of mass.
10. Collisions
Definition of collision; impact forces, conservation principles; one-dimensional elastic collisions; inelastic collisions; angular impulse, moment of body impulse; collisions between particles and rigid bodies.
11. Gravitation: phenomenology and Newton’s law
Motion of planets and satellites: Kepler laws; Newton’s gravitation law; measurement of constant G; inertial and gravitational mass; gravity near the Earth surface. Spherical distribution of mass (shells theorems). Gravitational potential energy, escape velocity: motion of artificial satellites. Central forces. Energy and orbits. Short account on gravitational field and potential.
12. Elastic properties of solids
Compression and tension, generalized Hooke’s law; Poisson law, volume deformation; shear deformation; torsion and torsion balance; uniform compression, pressure; plastic deformation.
13. Fluid statics
Static equilibrium of a fluid; Stevin and Pascal laws; atmospheric pressure: barometric equation; Archimedean principle and buoyancy. Short account on surface phenomena: surface tension; Laplace formula; capillary phenomena; Jurin’s law.
14. Fluid dynamics
Motion of an ideal fluid, lines of flow and tubes of flow; continuity equation; Bernoulli theorem. Short account on real fluids: laminar flow; viscosity; Hagen-Poiseuille law; turbulent flow, Reynolds number; motion of a body immersed in a fluid; mean resistance, lift force.
15. Oscillatory phenomena
One-dimensional oscillating systems; simple harmonic motion; energy in the simple harmonic motion; connection with the uniform circular motion; applications: simple, physical and torsion pendulums; damped free oscillations; forced oscillations and resonance.
Part III
16. Wave phenomena: elastic waves
Wave and wave function; phase and phase velocity; harmonic waves, plane waves; D’Alembert equation and its solutions; superposition principle; interference of harmonic waves; standing waves; beats. Propagation of a transverse wave on a string; standing waves on a string, harmonic series. Propagation of a pressure longitudinal wave in a gas; sound speed; sound wave intensity; standing longitudinal waves.
17. Thermodynamic systems and Thermology
Thermodynamic system and coordinates; equations of state; thermodynamic processes. Zero-th law of thermodynamics, thermal equilibrium. Temperature: scales and methods of measurements. Thermal expansion of solids.
18. Ideal and real gases
Macroscopic properties of gases. Kelvin temperature scale. Equation of state of an ideal gas. Constant-volume gas thermometer. Kinetic theory of gases: pressure and temperature of ideal gases. Mean free path of molecules. Real gases: pV diagrams, phase transitions and critical parameters; the Van der Waals equation of state.
19. Heat and first law of thermodynamics
Joule experiments; mechanical equivalent of heat. Reversible and irreversible processes. Heat; specific, molar and latent heat. Phase transitions. Calorimetry. Heat propagation. Work in thermodynamic processes. First law of thermodynamics. Examples: thermodynamic processes and cycles.
20. Applications of the first law of thermodynamics
Internal energy of an ideal gas. Molar heat of ideal gases. Molecular degrees of freedom and theorem of energy equipartition. Mayer relation. Isothermal, isobaric, isochoric and adiabatic process of an ideal gas.
21. Second law of thermodynamics
Heat engines and heat pumps. Thermal efficiency. Kelvin-Planck and Clausius enunciations of second law. Reversible Carnot cycle. Thermal efficiency of the Carnot cycle. Carnot’s theorem. Absolute temperature scale. Clausius’ theorem.
22. Entropy
Entropy and second law: the entropy-increase principle. Examples of determination of entropy variation for reversible and irreversible processes. Third law of thermodynamics (short account).
Bibliography
Elementi di Fisica – Meccanica - Termodinamica
P. Mazzoldi, M. Nigro e C. Voci
II edizione
Edizioni Scientifiche ed Universitarie (EdiSES), Napoli, 2008
ISBN: 9788879594189
FISICA 1
Meccanica - Acustica - Termodinamica
R. Resnick, D. Halliday, K. S. Krane
V edizione
Casa Editrice Ambrosiana (CEA), Milano, 2003
ISBN 8840812547
Fisica Generale: Meccanica e Termodinamica
S. Focardi, I. Massa e A. Uguzzoni
I edizione
Casa Editrice Ambrosiana (CEA), Milano, 1999
ISBN 8840812725
Teaching methods
Frontal lesson with help of audio-visual multimedial instruments
A part of the course will be devoted to the solution of problems and exercises, under the supervision of the teacher. A selection of exercises and problems for each topics will be posted on the course web page.
Assessment methods and criteria
Mid-term exams (in itinere evaluations) in written form and a final exam in (eventual) written and oral form will be given. A provisional grade will be proposed to the students if the comprehensive grade of mid-term exams is above a specific threshold. In such a case the final grade is assigned after an oral exam. The final exam, in written and oral form, is mandatory for the students having an insufficient grade of mid-term exams or don’t giving the intermediate exams.
Other information
Office hours: Wednesday, 10.30-11.30 or upon appointment
