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Second Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/64]  MATHEMATICS [64/00 - Ord. 2017]  PERCORSO COMUNE 12 96


Welcome to General Physics 1, the first physics course of the Physics and Mathematics Bachelors. As the instructor for this course, I look forward to helping you gain knowledge and develop habits of mind that will be useful in your career. My goals for this course are to engender the reasoning and problem solving skills, confidence, knowledge, and technical expertise that will help you become a leader in your profession. In particular, I hope to help you learn how to use scientific reasoning to reach informed decisions in real-world situations.
I take my teaching duties very seriously and will work very hard to attain these goals. I will make myself as accessible as possible — I do want to interact with all of you. I encourage you to stop by my office or call me; the number below is my cell phone. Call anytime. This document is meant to help you make the most of this course. It is divided into three parts: organization and philosophy, logistics, and policies. I look forward to working with you this semester!

Attending and successfully completing this course, you will …

(KNOWLEDGE AND UNDERSTANDING) acquire the basic knowledge on the foundations of classical mechanics: kinematics, dynamics, oscillations and waves. Furthermore, you will gain a basin knowledge of thermodynamics.

(SKILLS) learn how to define a solution of a problem as a procedure to develope and not simply as a memorized task to recall. In particular, you will be trained to solve a problem starting from a qualitative analysis classifying it on the basis of structural characteristics rather than on superficial aspects. You will be able to solve problems through the use of several tools as graphs, diagrams, limits, conservation laws.

(SELF-JUDGEMENT) be continuously stimulated to develope a critical approach on the understanding and elaboration of concepts. Through repeated stimuli, you learn to criticize unclear or ill-defined approaches. You will acquire the ability to establish in a self-confident way if the results makes sense (use of "common-sense").

(COMMUNICATION SKILLS) learn how to present ideas organizing their knowledge hierarchically. You will learn how to simplify complex problems in their essential terms. Through the exposure to interactive lectures and cooperative problem solving and cooperative problem solving, you will be trained to confront their ideas with their mates illustrating possible solutions to peers.

(LEARNING SKILLS) develope a methodology of study and analysis that will allow you to interprete and delve into problematics of classical physics that will be encounter through their studies.


1. Math: elementary math from high school: algebra and basic trigonometric formulas. Most of the needed math (elementary calculus) is developed during the course profiting also from the calculus and geometry courses.
2. Physics: there are no pre-requisites.


1. General concepts. Measurements, models, theories. Physics quantities. Space and time. Vectors and scalars. Vector operations. ¿

2. Kinematics and forces. Average velocity and instantaneous velocity; acceleration. One dimensional motion. Two dimensional motions. Harmonic motion. Dynamics of point particlesl force and mass; Newton laws. Reference systems; galileian transforms and limitations; non inertial reference frames; Centrifugal and Coriolis force. Friction. ¿

3. Work and energy. Work for constant and variable forces; kinetic energy; kinetic energy theorem. Conservative forces; potential energy. Potential energy diagrams. Mechanical energy conservation.

4. Gravitazione. LNewton gravitation law. Kepler laws. Force and potential energy for a homogeneous sphere.

5. Impulse and linear momentum. Impulse and linear momentum change for point particles. Momentum conservation for point particles. Variable mass systems. Elastic and inelastic collisions.

6. Rotational motion. Rotational variables: angular velocity and acceleration. Torque and angular momentum. Kinetic energy and moment of inertia. Rigid bodies. Angular momentum conservation; spinning top and gyroscope. Equilibrium of rigid bodies.

7. Oscillations. Harmonic oscillator: simple, damped and with sinusoidal force. Resonance, power. Systems with two degrees of freedom: coupled oscillators. Systems with an infinite number of degrees of freedom: standing waves; ideas on Fourier transform. Beats.

8. Mechanical waves. Propagation of waves. Wave equation. Dispersion; phase and group velocity. Principle of superposition. Transverse waves in a string. Longitudinal waves in a chain with springs and masses. Sound waves. Generation of sounds and relation to Fourier analysis. Speed of sound. Sound standing waves. Interference. Doppler effect.

9. Thermodynamics. Basic concepts: the idea of macrostate and microstate of complex systems. Temperature and heat as energy exchange; thermal equilibrium; thermometers. Thermal behaviour od solid and liquid bodies, gases. Perfect gas and absolute temperature. Element of kinetic theory: the Maxwell-Boltzmann distribution; kinetic interpretation of temperature; theorem of equipartition of energy. Thermodynamic transforms: isothermal, adiabatical. Thermal capacity and specific heat. First principle of thermodynamics and applications. Reversible and irreversible transforms. Second principle of thermodynamics: kelvin and Clasius statements; thermal engines. Carnot theorem and absolute temperature. Entropy.

Teaching Methods

The course structure is based on lectures and recitations. I will emphasize since the very beginning a particular methodology for problem-solving that is one of the central theme of the course. During the lectures I will illustrate repeatidly the application of that methodology through the solution of a least a non trivial problem each lecture. During the recitations, you will have the possibility to train together with your mates on the use of such a system under the guidance of the instructor and teaching assistants.

Further methological aspects point to alleviate some general problems of teaching at university level:

1. Even with well structured and clear lectures, a non negligible fraction of students migh remain substantially passive. They rarely ask questions. It is difficult to jugde how much you understand the lecture and if you find the course material interesting.

2. Some student don’t attend the lectures regularly.

3. In traditional lectures there are no tools to evaluate the understanding of the class on a daily basis.

Even outstanding teachers are often in trouble to keep a high level of attention during lecture time.
In order to alleviate such problems, E. Mazur, professor at the Harvard University, has developed a method termed peer instruction, which involves students in the learning process during the lectures, requiring them to concentrate on the basic concepts illustrated during the lecture.
During a lecture, concept tests are presented to the whole class, which are designed to illustrate the typical difficulties in the understanding of the lecture content. Students have to answer the question in real-time elaborating the answer together with mates.
This process will force you to think actively on the concepts developed during the lecture allowing you and the instructor to judge you understanding even before the end of the lecture time.
Quizzes are presented within the digital platform moodle. In this way you have the possibility to answer in real time via tablet or smartphone and you will receive an immediate feedback on the correctness of your answer.

This a teaching model originally developed at the University of Minnesota.
It is focused on the organization of recitations, where students are placed at the center of the action. In a typical recitation, students are divided in groups of 3-4 people and must solve in a cooperative way problems proposed by the instructor.
There are specific roles within a group: the manager, who proposes a solution, the criticist, who must contrast or propose alternative paths, the secretary. Roles are inverted at the next recitation.
I and the teaching assistants will guide you in finding the solution provind a coaching for the problem-solving.
That scheme encourage group collaboration (a basic aspect in the work inside a team in research or industry) and disfavour competition.
At the same time, students with different physics and math backgrounds must confront each other. Within the programme, rich context problems are presented, which will bring you in contact with problems or situations from the real like, learning general procedures to solve complex problems. Those will be useful to you in many other contexts, even outside physics.

Each week you will be given a problem to solve at home through the digital platform moodle. Homewroks are also uploded in moodle. Those homeworks enhance your discipline helping you to study on a regular basis. They will contribute to the examination score.

Each week you will be given a problem to solve at home through the digital platform moodle. Homewroks are also uploded in moodle. Those homeworks enhance your discipline helping you to study on a regular basis. They will contribute to the examination sc

Verification of learning

The final score is based on two written tests (the first at half semester, the second after the end of the course), an oral examination and completed homeworks.

Written tests allow the instructor to check the following dimensions:

1. Focus on the physics problem presented in the text:
- Evalute the essential and not so essential information
- Present a qualitative graphical description of the problem
- Show the data present in the text
- present clearly what is the question to answer
- define an approach on which the solution will be based

2. Describe the physics:
- provide a quantitative description of the physics situation with graphs, diagrams
- identify in unambiguous way all known and unknown variables
- identify the target quantity
- display all possible useful equations (physics laws)
3. plan the solution:
- write down a logical system of equations, the first containing the target quantity, that will allow the problem to be solved
- check that the system is sufficient (sufficient number of equations given the number of unknowns)
- write down verbally how you will solve the system

4. Execute the plan:
- Solve the equations for the tartet quantity as a funtion on the known variables
- Check that solution on a dimensional basis (dimensional analysis) makes sense
- Evaluate the numerical value of the traget wuantity using the numerical data provided by the problem

5. Evaluate the solution:
- Summarize if the question was answered
- Check if the units of the target quantity are correct
- Evaluate if the results is reasonable based on different arguments - for example using similar or simpler problems that you already solved, including also common sense and your personal experience

The oral examination will test the following dimensions:

1. Mastering the appropriate scientific language in the demonstration of some theoretical aspects of different subjects
2. Relating different concepts and knowledge in a comprehensive way

Homeworks will test the following dimensions:

1. following the course developments in a regular and disciplined way.

You can acquire up to 100 points:

• First written test: up to 30 points
• Second written test: up to 35 points
• Oral examination: up to 25 points
• Homeworks: up to 10 points

100 points corrispond to the score 30/30
55 points correspond to the score 18/30

There is no minimum score in the written tests to access to the oral examination. As a whole you will have to acquire a minimum score of 55 to pass the exam.
Furthermore, 15 extra points might be assigned by the instructor on the basis of a comprehensive evaluation of the written tests, oral examination and homeworks (that will allow the instructo to introduce some corrective weight in case of situations in which the second written test and the oral examinations are very positive, while the first writte test is not so positive).
The instructor will consider also the participation to the recitations, a fundamental activity for learing the problem-solving.


- Focus the physics: up to 20% of the total score of a problem

- Describe the physics: Descrivere la fisica: up to 25% of the total score of a problem

- Plan the solution: up to 25% of the total score of a problem

- Execute the plan: up to 20% of the total score of a problem

- Evaluate the solution: up to 10% of the total score of a problem


This is the reference text:
Fisica 1 - Halliday-Resnick-Krane (Ambrosiana)

Other books are used in some specific parts of the course (I will refer to them explicitely in due time):

- Feynman Lectures in physics
- Berkeley Physics Course vol. 1 (meccanica), vol. 3 (waves and oscillations)
- Termodinamica – Fermi

On moodle you can download detailed notes regarding oscillations and waves. These notes are the reference text for this part of the course.

More Information

What you can expect of me (and the rest of the teaching staff)

1. I will work very hard to make this course useful for you (but I cannot do the work and learn the material for you).

2. I will closely follow the class schedule as outlined on the course web site.

3. I will begin and end each class on time.

4. I will be available for assistance throughout the semester and look forward to meeting you in person.

5. I will do my best to promptly return your phone calls and answer your emails.

6. I will make sure assignments solutions and examinations are returned to you in a timely manner.

7. I will make sure the examinations are fair; our grading standards will likewise be fair and open.

8. I will listen to constructive comments about my teaching and be open to suggestions.

What I expect of you

1. You have made a conscious, informed choice to join this class. This means you have read this syllabus, understand the required workload, and meet the prerequisites.

2. You are coming to this class ready to learn, not just to earn a certain grade or meet a requirement.

3. You understand that you must accept responsibility for your own learning and take an active role in the learning process. You will therefore come to class prepared, having read the assigned course notes for understanding (but not necessarily understanding everything), and provide written feedback on what you need help with.

4. You will attend classes regularly being mentally present, come to class on time and not get up and leave before class ends.

5. You will participate fully to the recitations, come to class on time and not get up and leave before class ends.

6. You will have an active role in the discussions during lectures and recitations.

7. You will effectively and clearly communicate your understanding during lectures and recitations.

8. You will ask questions if something is unclear — in class, during office hours, by telephone, e-mail or online. Don’t wait until the end when there is little time left to address any problems.

9. You understand the benefits of collaboration and the strictly non-competitive nature of this course, and are willing to work with others in the classroom, in sections and laboratories, and on your homework assignments.

10. You will bring a positive attitude and share your personality, knowledge and skills with the rest of us throughout the semester.

11. You will be honest during examinations and you will do your best on the basis of your own knowledge only.

At the beginning of the course you will have to apply to the course “Generale 1” on the digital platform moodle. I will provide an access key.

Accessing moodle you will find notes (hand-written) on all the topics presented during lectures. You will have to read carefully these notes before each lecture.
You will also find all the problems presented in class with a solution, concept tests, homework assignments and computer animations/simulations.

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