Part I [3 CFU]
1. Mechanics: introduction
Classical Mechanics and Thermodynamics; Physics and measurements; physical quantities and units. Basic vector operations: 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: one-dimension
Material Point scheme. Position, velocity, acceleration vectors: constant-velocity and constant-acceleration motion. Free body fall. 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.
4. Kinematics of Material Point: two- and three-dimension
Cartesian representation and intrinsic representation of position, velocity and acceleration. Planar motions: projectile motion; circular motion; centripetal acceleration; angular Kinematics.
5. 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.
6. Relative motion
Inertial frames of reference: Galilean relativity. Non-inertial frames of reference, fictitious forces. Rotating frames of reference: Coriolis’ force. The earth frame of reference. Roto-translational motion.
7. 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.
Part II [3 CFU]
8. Dynamics of the systems of material points I
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. Koenig theorem for kinetic energy; kinetic energy and reference frames.
9. Dynamics of the rigid body I
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.
10. Dynamics of the rigid body II: statics and rolling motion
Centre of gravity. Static equilibrium of a rigid body. Rolling motion of rigid bodies. Work and kinetic energy in the rotational and roto-translational motions.
11. Dynamics of the systems of material points II: angular momentum
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; Koenig theorem for angular momentum. Angular momentum conservation.
12. 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.
Definition of collision; impact forces; impulse and impulse theorem; conservation principles in collisions; one-dimensional elastic collisions; inelastic collisions; angular impulse, moment of body impulse; collisions between particles and rigid bodies.
Part III [3 CFU]
14. 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.
15. Statics and dynamics of ideal fluids
Static equilibrium of a fluid; Stevin and Pascal laws; atmospheric pressure: barometric equation; Archimedean principle and buoyancy.
16. Oscillatory phenomena
One-dimensional oscillating systems; simple harmonic motion; ene