# 15749 - Mechanics (M-Z)

• Moduli: Annarita Margiotta (Modulo 1) Filippo Sala (Modulo 2)
• Campus: Bologna
• Corso: First cycle degree programme (L) in Physics (cod. 9244)
• from Sep 20, 2023 to Dec 22, 2023

## Learning outcomes

At the completing the course , the student has the basic knowledge of Newtonian mechanics of point particles and particle systems.

He/she has learned the use of the vector calculus and is able to apply the general concepts and the basic laws to solve simple problems of kinematic and dynamic

## Course contents

• Module 1

- Math complements. Vector calculus: vectors, vector operations (addition, subtraction, scalar and vector multiplications), properties of vectors, unit vectors. Simple derivatives and integrals of one-variable functions; concepts of partial derivatives of multivariable functions.

- Physical quantities. The concept of physical quantities, vector and scalar physical quantities. Dimensional analysis. Standard unit of measurement and systems of units of measurement ( S.I.). Homogeneity, isotropy and specular symmetry of space. Polar and axial vectors-

- Kinematics in one and more dimensions. Position, displacement, velocity and acceleration. Rotational variables (displacement, velocity and angular acceleration). Uniformly accelerated motion. Motion of projectiles. Uniform circular motion and centripetal acceleration. Circular motion in polar coordinates. Galilean transformations for inertial systems (position, speed, acceleration).

- Dynamics of material point. The laws of Newton for the forces. Mechanical forces (contact and not). Spring force. Static and dynamic friction.

Work and energy. Work of forces. Kinetic energy and theorem of live forces. Conservative and non-conservative forces. Definition of power.

- Potential energy for conservative forces. Circulation of a vector field of conservative forces Conservation of mechanical energy for a material point. Equilibrium: stable, unstable and indifferent.

- Non-inertial reference systems. Real and fictitious forces (drag, centrifugal and Coriolis). Centrifugal force.

- Static. Static equilibrium. Torque. Introduction on forces of compression and tension. Elasticity.

- Systems of particles. The center of mass. Newton's laws for particle systems. Momentum. Conservation of momentum. Internal and external forces to the system of material points and change in internal energy. Conservation of energy.

- Collisions between material bodies. Elastic and inelastic collisions. Collisions seen in different reference frames.

- Newton's Gravitation. Inertial and gravitational messes. Spherical body: total mass in its center. The acceleration of gravity at the Earth's surface. Gravitational potential energy.

- Kepler's Laws. Motion of the planets and Kepler's laws. Demonstration in terms of Newtonian mechanics of Kepler's empirical laws. Analytical determination of the Earth's elliptical orbit. Gravitational effects of massive objects such as black holes.Movement of the planets, and Kepler's laws

- Rotational dynamics: Rotational kinetic energy. Moment of inertia. Newton's laws for the rotary motion. The rotational kinetic energy conservation. Centripetal force. Work and power in rotations.

Roto-translational motion and rolling friction. Angular momentum and conservation of angular momentum: inertial axes of rotation; the spinner. Determination of G.

• Module 2

Problem solutions on the arguments of Module 1.

Since April 2023 is available a textbook that comes from this course:

• M. Spurio: Meccanica Newtoniana. EdiSes [https://www.edises.it/default/meccanica%20newtoniana.html]

The book fully covers the above programme, including the texts of the examination tasks of previous years.

In addition, several books can be used as a complement or supplement. Each has specific characteristics that make it valuable, and some critical aspects (in particular, some texts use obsolete notations)

• S. Focardi, I. Massa, A. Uguzzoni e M. Villa: Fisica Generale (meccanica e termodinamica), C.E.A. Milano
• R. Resnick, D. Halliday, K. Krane: Fisica 1, C.E.A. Milano
• P. Mazzoldi, M. Nigro, C. Voci: Fisica (Volume I), EdiSES Napoli
• Mencuccini, Silvestrini. Meccanica e Termodinamica, Casa Editrice Ambrosiana.

A cornerstone of physics (which I recommend to use in second reading).

• La Fisica di Feynman: Zanichelli.English version freely available from the website: https://www.feynmanlectures.caltech.edu/

For other textbooks that you may have available, consult the teacher (some General Physics books for other degree courses are not sufficiently thorough).

Finally, any book with exercises carried out (in the library there are many copies of many editions) and the exercises carried out in all recommended texts are indispensable for Module 2.

## Teaching methods

Lectures at the blackboard and solution of problems in the classroom.

## Assessment methods

The exam is unique for both modules and it consists of a written proof and an oral assessment. Six written proofs are scheduled in each academic year: three in the first Session (January/February); two in the second (June/July) and one in the third (September). The oral assessments start after the corrections of the writing proofs.

The written test concerns the solution of two distinct exercises. Each exercise is divided into points. As a rule, the difficulty is increasing (the first point is easy, the last is the most difficult). The total time available for the written test is 2 hours. To obtain the maximum score in the written test (31/30), the candidate must solve all the questions. Those requiring numerical solutions must be solved before setting the solution literally. The principles (or laws) applied must be mentioned, and the salient passages must be indicated schematically from the physical point of view. It is recommended to accompany the development with schematic drawings representing the situations. The results must be expressed with an appropriate number of significant digits. Sufficiency (18/30) is achieved by solving completely one of the two proposed exercises, or the initial parts (based on the difficulty) of the two proposed exercises.

A sufficient score in the written proof is a prerequisite for accessing the oral assessment, in one of the defined dates of the Session. The overall length of the oral assessment is about 30 minutes, divided between the teachers responsible for the two modules (the student is examined first by the teacher of one module and then by the teacher of the other). In the oral exam, the accuracy of the answers and definitions, the clarity and synthesis with which the topics are presented and the ability to connect the various topics will be assessed. Each teacher independently evaluate the test with a grade expressed with a maximum score of 31/30. A necessary condition for passing the oral assessment is that the student is evaluated with score >= 18 by both teachers. The verbalized final mark is the average of the three marks obtained (in the written test and in the two parts evaluated by the two oral teachers).

The student has a maximum of 3 days to decide to accept the final grade. After this period, failure to confirm acceptance is equivalent to refusal (which is recorded as such). According to the university teaching regulations, the refusal of the grade is possible at least once by the teacher. In case of refusal, the student will have to start from the written test.

## Teaching tools

Lectures will be given at the blackboard. Slides, drawings and short movies can be used to facilitate the understanding of some concepts and made available on the IOL website. Attending the courses is very useful, though it is not mandatory. Changes of the standard teaching organization are enivsaged as a consequence of the COVID-19 pandemic. Information and details will be provided in due time.

Students with disabilities are invited to contact the teacher in order to provide them with any kind of support useful to fully exploit the courses and to guarantee a proper access to the exams. No need to say that any private information will be treated as confidential.

## Office hours

See the website of Annarita Margiotta

See the website of Filippo Sala

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.