Physical quantities. Mechanics: reference frames, particle kinematics, relative motion. Particle dynamics: the principles of dynamics, motion in non-inertial frames, work and energy. Dynamics of extended systems: center of mass, angular momentum, conservation laws, cardinal equations of dynamics. Dynamics of rigid bodies. Short notes on fluid statics and dynamics. Thermodynamics: thermodynamic quantities, first and second principle.
Any text on basic mechanics and thermodynamics. For instance (in Italian):
M. Bruzzi, F. S. Cataliotti, D. Fanelli, Elementi di meccanica e termodinamica (Esculapio)
P. Mazzoldi, M. Nigro, C. Voci, Elementi di fisica: meccanica e termodinamica (EdiSES)
Learning Objectives
Acquired knowledge: Basics of classical mechanics, from particle kinematics and dynamics to the dynamics of extended system and rigid bodies. Basics of thermodynamics.
Acquired competence: Mastering of conceptual basis of mechanics and thermodynamics and their application to simple special cases.
Skills acquired (at the end of the course): Solution of elementary problem in particle and extended systems mechanics. Ability to apply the physical laws to simple real-world examples.
Prerequisites
Nothing but high-school mathematics.
Teaching Methods
6 CFU.
class hours: 54; extra recitation sessions (if possible) in the afternoon.
Extra material on the moodle online platform.
Further information
Office hours:
to be announced at the beginning of the course (one afternoon per week at the Engineering School in S. Marta or at the Centro didattico Morgagni).
Coordinates: Dipartimento di Fisica e Astronomia, Polo Scientifico di Sesto Fiorentino, stanza 304 (II piano)
tel. 0554572311 (int. 2311)
e-mail: lapo.casetti@unifi.it
Sito web: --
Type of Assessment
Written test, aiming at verifying the acquired skills, with emphasis on the solution of problems in mechanics. Oral test on all the subjects of the course, aiming at verifying the acquired knowledge and competence.
Course program
Introduction:
The physical law, observation and experiment. Physical quantities, measurements, units, operational definition. Uncertainties and their estimation. Vectors: definition, sum and composition, Cartesian components. Scalar and vector product.
Mechanics:
Kinematics.
Relativity of motion, reference frames. Position vector, definition of mass particle. Cartesian and polar coordinates. Vector equations of motion. Trajectory. Example: a circular motion. Motion in one dimension. Average speed. Velocity and derivatives. Acceleration. Inverse problem of kinematics. Integrals and integration rules. Uniform motion, harmonic motion, damped motion. Falling bodies. Kinematics in more than one dimension: velocity and acceleration vectors. Plane motions, falling bodies, circular motions. Tangent and centripetal acceleration. Angular velocity and acceleration. Relative motions: description of motion in different reference frames. Relative velocity and acceleration. Translations and rotations. Coriolis acceleration.
Point particle dynamics.
Force: intuitive concept and operational definition. Force vector and superposition principle. Weight and (ideal) constraint forces. Equilibrium on an incline. The principles of dynamics. First principle: inertial frames. Second principle: Newton's law and inertial mass. Solution of point particle mechanics problems. Elastic force, Hooke's law. Momentum. Meaning of Newton's law: integration of the equations of motion, numerical techniques. Central forces, gravitational force. Gravitational forces and Kepler laws. The pendulum, numerical solution and analytical solution for small oscillations. Experiment: measuring g with a pendulum. Damped oscillations and viscous forces. Static and dynamic friction. Dynamics in non-inertial frames: inertial forces. Translations and rotations. Effective weight in an accelerated elevator. Einstein's elevator. Rotating frames: centrifugal force, weightlessness on the space station. Coriolis force. The Earth reference frame.
Work and energy.
Work of a force. Kinetic energy. Work-energy theorem. Work done by elastic and gravitational forces. Conservative forces, potential energy. The pendulum. Conservative systems in one dimension.
Dynamics of extended systems.
Center of mass, momentum, internal and external forces. Motion of the center of mass. Conservation of total momentum in an isolated system. Elastic and inelastic collisions. Angular momentum and its evolution. Moment of a force. Conservation of angular momentum in an isolated system. Cardinal equations. Degrees of freedom. Kinetic energy of an extended system. Rigid bodies: definition and kinematics. Rotational motion, moment of inertia. Kinetic energy and conservation of mechanical energy in a rigid body. Rolling motion. Statics of rigid bodies. Short notes on the structure of matter. Solids, liquids and gases. Fluids: density and pressure. Stevin's law.
Thermodynamics:
Introduction and the kinetic theory of gases.
Necessity of a statistical description of the microscopic dynamics of a fluid. Kinetic theory of ideal gases. The ideal gas equation of state and temperature. Zeroth principle of thermodynamics. Relation between average kinetic energy of the molecules and temperature.
First principle of thermodynamics.
The Joule experiments and the equivalence between work and heat. The first principle of thermodynamics. Internal energy. Reversible and irreversible thermodynamic transformations. Transformations of an ideal gas: constant-volume, isobaric, isothermal, adiabatic transformations. Thermal machines and the Carnot cycle. Efficiency.
Second principle of thermodynamics.
Second principle of thermodynamics: Kelvin-Planck and Clausius formulations. Clausius' theorem. Entropy. Entropy and irreversibility, principle of entropy growth. Entropy variation in the free expansion of an ideal gas. Microscopic interpretation of the entropy, of the equilibrium states and of the second principle.