# UNIT 1

## Learning outcomes of the course unit

The objective of the Course is to provide a conceptual understanding of the fundamental laws of classical Mechanics, with particular focus on kinematics, Newton’s laws and conservation principles. The aim of the course is, from one hand, to give the analytical instruments that allows describing the dynamics of the most simple mechanical systems and examining their qualitative behaviour, even through the development of problem solving skill. On the other hand the course will provide the conceptual basis of the newtonian formulation of Mechanics, which is propedeutical to the formalizations described in more advanced courses.

## Prerequisites

Working knowledge of high school level algebra and trigonometry

## Course contents summary

Part I

1. Mechanics: introduction

Classical Mechanics; Physics and measurements; physical quantities and units. Elements of vector algebra: 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-dimensional motion

Material Point scheme. Position, velocity, acceleration vectors: constant-velocity and constant-acceleration motion. Free body fall. Simple 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; impulse and impulse theorem.

4. Two- and three-dimensional motion

Intrinsic representation of the trajectory, velocity and acceleration; constant-velocity and constant-acceleration motion. 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 motions

Inertial frames of reference: galileian relativity. Non-inertial frames of reference, fictitious forces. Rotating frames of reference: Coriolis force. The earth frame of reference. Frames of reference both rotating and translating.

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; general treatment of one-dimensional and three-dimensional conservative systems.

## Recommended readings

Suggested textbooks:

Elementi di Fisica – Meccanica - Termodinamica

P. Mazzoldi, M. Nigro e C. Voci

II edizione

Edizioni Scientifiche ed Universitarie (EdiSES), Napoli, 2008

ISBN: 9788879594189

FISICA 1

Meccanica - Acustica - Termodinamica

R. Resnick, D. Halliday, K. S. Krane

V edizione

Casa Editrice Ambrosiana (CEA), Milano, 2003

ISBN 8840812547

Fisica Generale: Meccanica e Termodinamica

S. Focardi, I. Massa e A. Uguzzoni

I edizione

Casa Editrice Ambrosiana (CEA), Milano, 1999

ISBN 8840812725

## Teaching methods

Teaching methodology:

Frontal lesson with help of audio-visual multimedial instruments

esercitazioni in aula (soluzione problemi ed esercizi proposti)

A part of the course will be devoted to the solution of problems and exercises, under the supervision of the teacher. A selection of exercises and problems for each topics will be posted on the course web page.

Evaluation methods:

Mid-term exams (in itinere evaluations) in written form and a final exam in (eventual) written and oral form will be given. A provisional grade will be proposed to the students if the comprehensive grade of mid-term exams is above a specific threshold. In such a case the final grade is assigned after an oral exam. The final exam, in written and oral form, is mandatory for the students having an insufficient grade of mid-term exams or don’t giving the intermediate exams.