MECHANICS OF SYSTEMS AND THERMODYNAMICS
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Knowledge of the fundamental laws of point-particle mechanics (esp. dynamics); linear algebra; differential calculus of functions of a single real variable.
Written examination (compulsory), possible viva examination. The written test includes two to four problems to be solved and the discussion of the theory connected to two course topics.
Aim of this course module is to provide detailed elements of particle systems’ and rigid-bodies’ dynamics, a description – mostly phenomenological – of elasticity phenomena, an introduction to the statics and dynamics of fluids and an introduction to kinetic theories and (equilibrium) thermodynamics. It is expected from the student a reasonably deep understanding of such topics and to be able to solve set problems in these areas of classical physics.
The rigid body. Translational motion and first cardinal equation. Kinematics of a rigid body with a fixed point. Rotational motion around a fixed axis, kinetic energy and moment of inertia. Calculation of the moment of inertia for simple rigid bodies. Relationship between angular momentum and angular velocity: tensor of inertia. Principal triad of inertia. Solution of dynamical problems through equations of motion and conservation laws. Pure rolling motion. Gyroscopes: free Poinsot motion. Heavy gyroscopes in rapid rotation. Rigid body statics.
Deformable rigid bodies: linear regime, elastic and plastic regime. Young modulous and Poisson coefficient. Compressibility modulus and shear modulus. Mechanical hysterises.
Statics of liquids (and fluids). Pressure: Stevino’s law, Archimede’s principle, Torricelli experiment. Stability of floating bodies: metacenter.
Surface (and capillary) phenomena: surface tension. Bubbles. Contact angle, capillarity.
Fluid dynamics: mass conservation, material derivative, Cauchy and Euler equations. Bernoulli theorem and applications. Viscous Newtonian fluids. Poiseuille law. Motion of a viscous fluid, limit velocity.
Thermodynamics. Concept of equilibrium. Work and heat. The principles of thermodynamics. Ideal gas. Carnot’s engine cycle. Concept of entropy. Statistical meaning of entropy. Thermodynamic potentials. Kinetic theory of gases. Maxwell postulates. Approach to equilibrium. Detailed balance. Master equation. Elements of statistical mechanics.
The rigid body. Translational motion and first cardinal equation. Kinematics of a rigid body with a fixed point. Rotational motion around a fixed axis, kinetic energy and moment of inertia. Calculation of the moment of inertia for simple rigid bodies. Relationship between angular momentum and angular velocity: tensor of inertia. Principal triad of inertia. Solution of dynamical problems through equations of motion and conservation laws. Pure rolling motion. Gyroscopes: free Poinsot motion. Heavy gyroscopes in rapid rotation. Rigid body statics.
Deformable rigid bodies: linear regime, elastic and plastic regime. Young modulous and Poisson coefficient. Compressibility modulus and shear modulus. Mechanical hysterises.
Statics of liquids (and fluids). Pressure: Stevino’s law, Archimede’s principle, Torricelli experiment. Stability of floating bodies: metacenter.
Surface (and capillary) phenomena: surface tension. Bubbles. Contact angle, capillarity.
Fluid dynamics: mass conservation, material derivative, Cauchy and Euler equations. Bernoulli theorem and applications. Viscous Newtonian fluids. Poiseuille law. Motion of a viscous fluid, limit velocity.
Thermodynamics. Concept of equilibrium. Work and heat. The principles of thermodynamics. Ideal gas. Carnot’s engine cycle. Concept of entropy. Statistical meaning of entropy. Thermodynamic potentials. Kinetic theory of gases. Maxwell postulates. Approach to equilibrium. Detailed balance. Master equation. Elements of statistical mechanics.
Lectures from the course-holder, including both explanation of theory and complements, examples.
Occasionally, other textbooks will be used (in parts) and the course holder's own lecture notes; photocopies and scans of the notes will be distributed.