# MECHANIC OF POINT, SYSTEMS AND FLUIDS MOD. II

MECHANICS OF A SINGLE POINT, SYSTEMS AND FLUIDS

MOD. 1

Prerequisites:

Physics and Mathematics at high school level

MOD. 2

Prerequisites: Basic laws of mechanics. Linear algebra. Basic notions of calculus.

MECHANICS OF A SINGLE POINT, SYSTEMS AND FLUIDS

MOD. 1

Teaching objectives and expected learning outcomes:

The goal is to provide a detailed picture of the kinematics and dynamics of a single point. In particular we stress on conservation of energy and momentum, specifically in the case of the gravitational field. We expect to reach full comprehension of the basic concepts and the capacity to solve problems .

MOD. 2

Teaching objectives and expected learning outcomes:

The goal is to provide a detailed knowledge of the mechanics of systems of particles and rigid bodies, and an introduction to fluid statics and dynamics. The student is expected to acquire a thorough understanding of such items, and the capability to solve problems.

MECHANICS OF A SINGLE POINT, SYSTEMS AND FLUIDS

MOD. 1

Course program:

Basics of elementary geometry and trigonometry.

Systems of units: MKS, cgs.

Overview on linear dimensions: nuclei, atoms, meter and the Earth radius, the Galaxy and the Universe.

Mass: proton and the Avogadro number, electron, Earth, Galaxy and Universe.

Density: water, air, Earth , Sun and Universe.

Systems of coordinates: Cartesian, cylindrical and spherical.

Translation and Rotation.

Basics of Calculus (derivatives and integrals).

Trajectory (one dimension).

Velocity and acceleration (od)

Uniform motion, uniformly accelerated motion, harmonic motion.

Kinetic energy and momentum (od).

One dimension elastic scattering.

Examples of inelastic scattering.

Vectors, vector algebra, vectorial operators.

Kinematics in 2,3 dimensions.

Circular motion and centripetal acceleration.

The balistic problem.

Normal and tangential acceleration.

Elastic scattering in two dimensions.

First and second principle of dynamics.

Weight: the equivalence principle.

Normal forces: motion on an inclined plane.

Tension: the Atwood machine.

Elastic forces: the Hook law.

The pendulum

The third principle of dynamics, and the conservation of momentum.

Newton’s gravitation

Measure of G; The Cavendish experiment.

Measure of mass and density of Earth and Sun

Kepler’s laws with focus on circular orbits.

Work of forces and the theorem of kinetic energy.

Conservative forces and potential energy.

Free fall velocity.

Geostationary orbits.

The virial theorem.

Frictional and viscous forces.

Non inertial frames: Mach principle.

Apparent forces: centrifugal and Coriolis forces.

The Foucault pendulum

Oscillations around a point of stable equilibrium: the case of nuclear forces.

Type of didactical activities:

Lessons, exercises, exercises at home.

MOD. 2

Course program:

Cardinal equations for a system of particles. Center of mass. Description of continuous systems.

Kinematics and dynamics of rigid bodies: translational and rotational motion. Tensor of inertia, angular momentum. Principal axes, Euler equations, gyroscopes.

Basic notions of elasticity.

Statics of fluids, pressure, Stevino’s law, buoyancy.

Surface effects.

Basics of fluid dynamics: conservation of mass, Euler equation. Stationary phenomena: Bernoulli theorem. Viscosity.

Type of didactic activities: Recitation class, with a number of discussed problems.

MECHANICS OF A SINGLE POINT, SYSTEMS AND FLUIDS

MOD. 1

Texts and teaching material:

Reference text: G. Rosati : Fisica Generale 1

Complementary texts: Berkeley Physics (Mechanics); The Feynmann Lectures (vol 1); Halliday , Resnick Walker , Fundamentals of Physics (for the exercises).

Verification of learning skills:

Written examinations consisting in the solution of simple problems are proposed during and at the end of course. The student can ask for an exam. The student in group of 3 -4 will perform a simple experiment, e.g. regarding the pendulum, and prepare a written report. They are also requested to study in some detail a classic experiment e.g. Cavendiish, Foucault, Eotovos.

MOD. 2:

Texts and teaching materials:

Pdf notes of classes, G. Rosati “Fisica generale”

Verification of learning skills:

Final written examination.