B5533 - I PRINCIPI DEL MOTO

Learning outcomes

At the end of the course the student has acquired the mathematical physics tools necessary to understand the founding concepts of classical, relativistic and random mechanics. He/she is able to solve elementary problems on the motion of the point and to identify the physical origins of some classic mathematical problems. He/she can present scientific material and arguments, orally or in writing, in a clear and understandable way.

Course contents

1. The experimental method, measurements, and the International System of Units (SI). Equation of motion: average and instantaneous velocity and acceleration. Uniform and uniformly accelerated motion. The inverse problem of Mechanics.
   
   
2. Review of vectors, plane angles, dot product, and cross product. Motion in Euclidean affine space and Cartesian reference frames. Curvilinear trajectories. Intrinsic decomposition of velocity and acceleration vectors.
   
   
3. Projectile motion, circular motion, angular velocity, and angular acceleration. Periodic motions. Polar coordinates and unit vectors. Polar decomposition of velocity and acceleration.
   
   
4. Newton’s laws and inertial reference frames. Forces: gravity, constraint forces, tensions, static and kinetic friction, drag forces, and elastic forces. Harmonic oscillator and pendulum motion.
   
   
5. Work, force fields, kinetic energy, and the work–energy theorem. Conservative forces, potential energy, and mechanical energy. Qualitative analysis of one-dimensional motions.
   
   
6. Newtonian gravitational force. Spherically symmetric central fields and potential energy. Kepler’s laws. Field flux and the Newton–Gauss theorems.
   
   
7. Reference frames in relative motion. Galilean transformations. Non-inertial reference frames. Rotating systems. Apparent forces. Centrifugal force and Coriolis force.
   
   
8. Systems of particles. Center of mass. Linear momentum and angular momentum. Center-of-mass theorems. Internal and external forces. Fundamental laws of dynamics for systems. Energy of particle systems and König’s theorem. Two-body systems. One-dimensional collisions.
   
   
9. Rigid bodies. Body-fixed reference frames. Axial moments of inertia and the Huygens–Steiner theorem. Rotation about a fixed axis, rotational kinetic energy, and rolling motion. Inertia tensor, principal axes of inertia, and free rotations.
   
   
10. Postulates of Relativity. Lorentz transformations. Minkowski spacetime. Length contraction and time dilation. Simultaneity and causality.
    
    
11. Random walk. Theory of independent steps. The law of Brownian motion.

Readings/Bibliography

- "Lezioni di Meccanica Elementare e oltre" di F.Camilli, P.Contucci; Bologna University Press, ISBN 979-12-5477-191-4

- Focardi, Massa, Uguzzoni -"Fisica Generale: Meccanica e termodinamica" (Casa Editrice Ambrosiana)

Suggested readings:

• "Fisica con fisica moderna" di D. Giancoli. Zanichelli.

• "La Fisica di Feynman", R. Feynman, Zanichelli Ed.

• "Cos'e' la matematica", R.Courant, E. Robbins, Boringhieri Ed.

Teaching methods

Each lesson will consist of an illustration of the concepts and their discussion through examples, followed by problem-solving and exercises.

Assessment methods

Written Examination:

The written examination consists of solving a set of problems, which may also include more theoretical questions, covering the topics discussed during the course. The written examination is graded on a 30-point scale.

Oral Examination:

The oral examination is intended to further assess the student's reasoning skills and understanding of the course topics. Students are admitted to the oral examination with a score of at least 15/30 on the written examination.

• For students who obtain a score between 15/30 and 20/30, the oral examination is mandatory.
• For students who obtain a score between 21/30 and 25/30, the oral examination is optional.
• For students who obtain a score between 26/30 and 30/30, the oral examination is mandatory only if they wish to obtain a final grade higher than 25/30. Alternatively, students may choose not to take the oral examination and accept a final grade of 25/30.

Final Grade:
For students who take the oral examination, the final grade will be an overall assessment that also takes into account the score obtained in the written examination.

Teaching tools

- Lecture notes;

- Weekly exercise sheets;

Office hours

See the website of Daniele Tantari

See the website of Francesco Camilli