# PHYSICS 1

## Learning outcomes of the course unit

The objectives of the Course are:

- to provide a conceptual understanding of the fundamental laws of classical Mechanics, including systems dynamics, and of Thermodynamics, with particular focus on kinematics, Newton’s laws and conservation principles;

- to develop some understanding of main aspects of the dynamics of rigid bodies;

- to treat the mechanics of continuum systems (fluids and elastic properties of solids), the thermology and the thermodynamics from a phenomenological viewpoint;

- to initiate the description of oscillatory and wave phenomena and of gravitation.

The aim of the course is, from one hand, to give the analytical instruments that allows describing the dynamics of the most simple mechanical and thermodynamic 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 preparatory to the formalizations described in more advanced courses.

## Prerequisites

- Working knowledge of high school level algebra and trigonometry;

- Differential and integral calculus

- Principles of analytical geometry and of elementary vector analysis

## Course contents summary

1. Mechanics: introduction

2. Kinematics of Material Point: one-dimensional motion

3. Dynamics of material point: Force and Newton’s laws

4. Two- and three-dimensional motion

5. Applications of Newton’s laws

6. Relative motions

7. Work and mechanical Energy

8. Dynamics of the systems of material points

9. Dynamics of the rigid body I: moment of inertia and Newton’s 2nd law

10. Dynamics of the rigid body II: statics and rolling motion

11. Dynamics of the rigid body III: angular momentum

12. Energy conservation

13. Collisions

14. Short account on special relativity

15. Gravitation: phenomenology and Newton’s law

16.Gravitation: outline of the formal treatment

17. Elastic properties of solids

18. Fluid statics

19. Fluid dynamics

20. Oscillatory phenomena

21. Wave phenomena

22. Elastic waves

23. Thermodynamic systems and Thermology

24. Ideal and real gases

25. Heat and first law of thermodynamics

26. Applications of the first law of thermodynamics

27. Second law of thermodynamics

28. Entropy

## Course contents

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.

Part II

8. Dynamics of the systems of material points

Motion of a system of particles; center of mass and its motion; Newton’s 2nd law for a system of particles; conservation of linear momentum; center of mass reference system; work-energy theorem; Koenig theorem for kinetic energy; kinetic energy and reference systems. Variable-mass systems.

9. Dynamics of the rigid body I: moment of inertia and Newton’s 2nd law

Rigid body scheme, density, center 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; center of gravity.

10. Dynamics of the rigid body II: statics and rolling motion

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 rigid body III: 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. Precessional motions: gyroscopes, spinning top.

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 center of mass. Heat and the first principle of thermodynamics.

13. Collisions

Definition of collision; impact forces, conservation principles; one-dimensional elastic collisions; inelastic collisions; angular impulse, moment of body impulse; collisions between particles and rigid bodies.

14. Short account on special relativity

Difficulties of classical physics: time, length, speed, energy, light. The postulates of special relativity; consequences of the postulates: time dilation and length contraction; relativistic composition of velocities. Lorentz transformations; measurement of the space-time coordinates of an event; speed transformation; relativity of simultaneity. Relativistic linear momentum;

## Recommended readings

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

Frontal lesson with help of audio-visual multimedial instruments

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.

## Assessment methods and criteria

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.