CODE 108699 2024/2025 6 cfu anno 1 INGEGNERIA GESTIONALE 10716 (L-9) - GENOVA FIS/01 GENOVA 2° Semester Questo insegnamento è un modulo di: AULAWEB

## AIMS AND CONTENT

### LEARNING OUTCOMES

The course provides an introduction to the phenomenology and the mathematical formulation of the laws of classical mechanics. The student will acquire the scientific-technical methodology necessary to deal with the problems of physics in quantitative terms.

### AIMS AND LEARNING OUTCOMES

The course aims to impart knowledge of the fundamental laws of mechanics. Its educational objective is to foster a deep understanding of these concepts and the ability to apply them in solving simple problems. This entails developing the skill to model problems using the fundamental laws introduced throughout the course. It is worth emphasizing that, in the realm of physics, comprehending a concept is inherently intertwined with the capacity to effectively employ it in relatively straightforward scenarios.

### TEACHING METHODS

Lectures and exercises in class

### SYLLABUS/CONTENT

1. Kinematics of particles:
Reference frames. Trajectory. Degrees of freedom. Parametric equations of motion. Rectilinear motion. Average and instantaneous velocity and acceleration. From acceleration to velocity and position. Free fall. Motion in the plane and in space. Kinematic vectors in Cartesian and polar coordinates. From acceleration to velocity and position. Planar motion: projectile motion, circular motion. Radial and tangential acceleration. Tangential and normal acceleration to the trajectory in any planar motion. Relativity of kinematic quantities. Transformation of kinematic quantities between reference frames in uniform rectilinear relative motion, Galilean transformations. Uniformly accelerated relative rectilinear motion. Relative circular motion. Roto-translatory relative motion (overview).

2. Dynamics of particles:
Principle of relativity. Newton's first law and inertial reference frames. Newton's second law. Action and reaction. Applications: weight force; normal reaction of the plane; static and dynamic friction forces; viscous friction; tension in ropes. Elastic forces and simple harmonic oscillator. Newton's law of universal gravitation and fundamental forces. Inertial mass and gravitational mass. Dynamics in non-inertial reference frames (overview). Impulse-momentum theorem. Conservation of momentum. Angular momentum theorem. Conservation of angular momentum. Case of central forces. Work. Work-energy theorem. Power. Conservative forces and potential energy. Conservation of mechanical energy. Potential energy associated with central forces. General discussion of 1D conservative systems based on the knowledge of U(x) and E: equilibrium conditions.

3. Dynamics of discrete and continuous systems:
External and internal forces within the system. Center of mass (c.m.). Simple examples of calculating the position of the c.m. Momentum of a system. First cardinal equation and motion of the c.m. Conservation of momentum. Angular momentum of a system. Moments of internal and external forces. Second cardinal equation. Conservation of angular momentum. Isolated systems and the third law of dynamics. Kinetic energy. Center of mass reference frame. Koenig's theorems for kinetic energy and angular momentum. Collision processes between particles; elastic and inelastic collisions; collisions in the c.m. reference frame. Simple rigid systems. Parallel forces: center of gravity. Rotation about axes of symmetry: moment of inertia, axial moment, and the second law for rotational motion. Calculation of moment of inertia for simple bodies. Parallel axes theorem. Rotation of non-symmetric rigid bodies about an axis passing through the c.m. Precession. Role of constraint reactions. Kinetic energy and work in rotational motion. Roto-translatory motion: pure rolling. Simple rigid body collision processes. Statics of rigid bodies: role of constraint reactions.

Any edition of a good university level general physics book can be used. For example:

David Halliday, Robert Resnick, Kenneth Krane - Fisica, vol. 1

Paolo Mazzoldi, Massimo Nigro, Cesare Voci - Elementi di Fisica. Meccanica e Termodinamica (qualsiasi edizione)

## LESSONS

### Class schedule

The timetable for this course is available here: Portale EasyAcademy