# PHYSICS 1

## Learning outcomes of the course unit

At the end of the course, the student is expected to be able to:

[Knowledge and understanding]

- know the fundamental laws of classical Mechanics of material point and of Thermodynamics, with particular focus on kinematics, Newton’s laws and conservation principles;

- know the main aspects of the dynamics of systems of material points and of rigid bodies, gravitation, oscillatory and wave phenomena and of the Theory of Special Relativity;

- explain the origin of the depicted phenomena on the basis of experimental findings and of mathematical methods, on the basis of the outlined physical models;

[Applying knowledge and understanding]

- assess similarities and differences between physical systems, methodologies to be applied, approximations and mathematical methods to be used;

- apply knowledge and understanding by demonstrating ability to solve exercises and problems of classical mechanics and thermodynamics;

[Learning skills]

- interpret and understand the content of basic texts on topics of classical mechanics and thermodynamics;

- utilize the methodological approach of the Newtonian formulation of Mechanics as a conceptual basis for the formalization of topics in Physics addressed in more advanced courses;

[Making judgments]

- recognize and draw connections not only between different parts of the course but also with the basic concepts acquired in other courses (for example maths and chemistry) for developing an ability for autonomous judgment based on an enlarged knowledge of the various aspects of the problem under consideration;

- evaluate critically the validity limits of the developed models;

[Ability to communicate]

- communicate the product of this study in a clear, synthetic and effective manner, using the correct jargon of Physics, in order to translate correctly even complex concepts in understandable language.

## Prerequisites

• Working knowledge of high school level algebra and trigonometry;

• Working knowledge of differential and integral calculus;

• Principles of analytical geometry and of elementary vector analysis.

## Course contents summary

Part I

1. Mechanics: introduction and vector calculus

2. Kinematics of material point: one-dimension

3. Kinematics of material point: two- and three-dimension

4. Dynamics of material point: force and Newton’s laws

5. Applications of Newton’s laws

6. Relative motion

7. Work and mechanical energy

Part II

8. Dynamics of the systems of material points I

9. Dynamics of the systems of material points II

10. Dynamics of the rigid body I

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

12. Dynamics of the rigid body III: angular momentum conservation

13. Energy conservation

14. Collisions

Part III

15. Gravitation I: phenomenology and Newton’s law

16. Gravitation II: notes on the formal treatment

17. Oscillatory phenomena

18. Essentials on the mechanical properties of solids

19. Statics and dynamics of ideal fluids

20. Essentials on the mechanical properties of real fluids

21. Wave phenomena

22. Elastic waves

Part IV (only for students of the Degree in Physics)

23. Thermology and ideal gases

24. Heat and first law of thermodynamics

25. Applications of the first law of thermodynamics

26. Second law of thermodynamics

27. Entropy

28. Essentials on the Special Relativity theory I: kinematics

29. Essentials on the Special Relativity theory II: linear momentum, energy

## Course contents

Part I [3 CFU]

1. Introduction and recalls of vector analysis

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. Kinematics of Material Point: two- and three-dimension

Cartesian and polar coordinates representation, intrinsic representation of trajectory, position, velocity and acceleration. Planar motions: projectile motion; circular motion; centripetal acceleration; angular Kinematics.

4. 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, angular momentum and its conservation, theorem of angular momentum.

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

System of material points, centre of mass and its motion; theorem of centre of mass motion; linear momentum and its conservation; centre of mass reference system. Two-bodies system: relative velocity and acceleration; momentum and energy; motion equation. Variable-mass systems; rocket equation.

9. Dynamics of the systems of material points II: angular momentum, work and energy

Angular momentum of a system of particles; theorem of angular momentum; angular momentum and frames of reference. Dynamics fundamental equations and Newton’s third law. Work and work-energy theorem. Koenig theorem for kinetic energy; kinetic energy and reference frames.

10. Dynamics of the rigid body I

Discrete and continuous system; rigid body scheme, density, centre of mass; translation, rotation and roto-translation: kinematics of rigid bodies; moment of inertia; Huygens-Steiner’s theorem; axial angular momentum, precession of angular momentum; law of motion for rigid rotation around a fixed axis.

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

System of parallel forces and 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.

12. Dynamics of the rigid body III: angular momentum conservation

Components of the axial angular momentum, precession; rotational equilibrium. Angular momentum conservation. Koenig theorem for the angular momentum. Short account on precessional motion of rigid bodies: gyroscopes, spinning top; nutation.

13. 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.

14. Collisions

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

## Recommended readings

Suggested textbooks

• Fisica Generale. Meccanica – Termodinamica

P. Zotto, S. Lo Russo, P. Sartori

I edizione

Edizioni La Dotta, Casalecchio di Reno (Bologna), 2016

ISBN 978-88-98648-37-5

• Fisica Generale: Meccanica e Termodinamica

S. Focardi, I. Massa, A. Uguzzoni e M. Villa

II edizione

Casa Editrice Ambrosiana (CEA), Milano, 2014

ISBN 978-8808-18215-9

• 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 978-8808-08611-2

Note on textbook choice

The textbooks are obviously alternative, although in part complementary. The students must make the choice based on personal preferences and previous preparation. Resnick’s textbook is less formal and with a ”tutorial" style, with many exercises and examples; Focardi’s and Zotto’s textbooks are most formally accurate, with some examples and a few or nothing exercises; Mazzoldi’s textbook, while presenting examples and exercises, is rather synthetic though preserving a formal exactness.

## Teaching methods

The teaching methodology will be based primarily on frontal lecturing, with help of audio-visual multimedia instruments. The lectures will be organized face-to-face, with the possibility of attending them even from a distance synchronously (during class hours), through the Teams platform. The links to the recorded videos of the lectures will then be placed on the Elly page of the course (Department of Mathematical, Physical and Computer Sciences: https://elly2020.smfi.unipr.it/course/view.php?id=17), in order to allow to attend the lectures also in asynchronous mode.

The slides used to support lessons will be uploaded weekly on the Elly platform. To download slides, the students need to enrol in the course on Elly.

The second part of the lesson will normally be devoted to the solution of problems and exercises, under the supervision of the teacher. A selection of exercises and problems for each topic will be uploaded weekly on the Elly platform. The teacher will be available for clarifications regarding both theory and exercises, for individual students or groups of students, through video-meeting on the Teams platform, both during reception hours and by appointment. There will also be additional training sessions held by Tutors in preparation for the mid-term exams. These exercises, at least for the first semester, will be carried out in video-meeting on the Teams platform.

## Assessment methods and criteria

Evaluation methods:

The assessment of the acquisition of learning outcomes will take place through mid-term exams in written form (which will require registration on the ESSE3 web platform) and a final exam in oral and (if necessary) written form. A provisional grade will be proposed to the students if the comprehensive grade of the mid-term exams is above a specific threshold (average grade equal to or higher than 18/30). In order to sustain the oral exam, which will aim to assign the final grade, students must enrol for it (registration to the oral exam on ESSE3). The exemption from the written test examination and the assigned provisional grade will retain their validity for all the exams of the 2020/21 academic year.

The final exam, in written and oral form, is mandatory for the students having an insufficient grade of mid-term exams or do not giving the intermediate exams. In such a case, the students have to register to the written exam on ESSE3 and they will be considered eligible for the oral exam if they reach an assessment equal to or greater than 18/30.

During each of the written mid-term exams, the student will be asked to:

- demonstrate the knowledge and understanding of specific course topics, through open questions, which will require the use of the technical correct jargon of Physics and synthesis skills (weight 15 points);

- demonstrate the ability to apply knowledge and understanding by solving some problems related to specific course topics (weight 15 points).

The written mid-term exams will be evaluated in 30-point scale. Each written exam will last 150 minutes and will have to be done without the help of notes or books but with the help of a pocket calculator. The results of written exams will be notified by posting them on ESSE3. The final written exam will have a similar structure but problems and questions will cover all the topics of the course program and will last 180 minutes.

During the oral exam, the student will be asked to:

- demonstrate the development of an autonomous judgment based on the knowledge and understanding of the fundamental laws of classical mechanics and of thermodynamics, by discussing the carried out written exams (final or mid-term) and deepening of theoretical arguments, drawing connections between the various parts and with basic concepts acquired in other courses;

- be able to use the correct technical-specialist language of Physics so that complex concepts can be translate correctly into an understandable language.

The oral exam will be evaluated in 30-point scale. The final grade will result from the arithmetic mean of the grades of written final exam (or the comprehensive grade of the mid-term written exams) and oral exam.

If due to the persistence of the health emergency it is necessary to integrate the conduct of the exams with the remote modality, the mid-term and the final written exams will be carried out remotely (via Teams and Elly) and will require registration on ESSE3. The tests on the Elly platform will consist of multiple choice quizzes, which will require the solution of exercises, and numerical answer quizzes, which will require the solution of structured problems, consisting of some questions. Detailed information on how the mid-term and the final written exams are carried out will be sent to students enrolled on ESSE3. The results of the exams will be notified by posting them on ESSE3. The oral exam will be carried out remotely (via Teams).

## Other informations

Office hours: Monday, 12.00-13.00 or upon appointment