# MECHANIC OF POINT, SYSTEMS AND FLUIDS MOD. I

Basic elements of mathematics and geometry at the secondary school level.

Aim of this course module is to provide detailed elements of kinematics and dynamics of point-like particles, including gravitational systems, 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.

At the end of the course the successful student will be able

1) to master the main concepts introduced in the course and solve problems;

2) to acquire critical sensibility and scientific method;

3) to develop simple models to describe physical processes.

First term (7 credits; Prof. A. Parola)

- Introduction. Measuring physical quantities. Units of measurement (MKS,cgs) (2 h)

- Vectors: sum, scalar product, vector (cross) product. Coordinate systems: Cartesian and polar. Elementary introduction to differential calculus (6 h).

- Kinematics. Trajectory and the description of motion. Velocity and acceleration. Uniform motion, uniformly accelerated motion, harmonic motion. Uniform circular motion, centripetal acceleration. Tangential and normal acceleration. Reference systems: principle of relativity. Relationship between different reference systems (10 h).

- Dynamics. First and second laws of dynamics. Third law and momentum conservation. Weight. Rheonomic constraints: inclined plane. Elastic forces: Hooke's law.The pendulum. Tensions. Atwood machine (10 h).

- Frictional laws and viscous forces. Some example of motion in the presence of friction and viscosity. Fictitious forces (4 h).

- Impulse-momentum theorem.Variable masses. Kinetic energy, work: work-energy theorem. Conservative forces, potential energy. Conservation of mechanical energy. Angular momentum. Central forces and conservation of angular momentum (10 h).

- Gravitation. Equivalence principle. Newton's law of gravitation. Measuring G: the Cavendish experiment. Gravitational potential energy.Kepler laws. Center of mass and reduced mass. Gauss theorem. Motion of a point in a gravitational field (10 h).

- Elastic and inelastic collisions. Dynamics of systems of points: Newton's equations and the definition of torque (4 h).

Second term (9 credits; Prof. G. Jug)

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 regimes. 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.

Text books: G. Rosati, “Fisica Generale 1” (and lecturer’s notes). M. Fazio, “Termodinamica”

Supplementary reference: The Feynmann Lectures, Vol. 1

Exercise book: S. Rosati, R. Casali, “Problemi di Fisica Generale”