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. Measurements and international system. Mean and instantaneous speed. Uniform rectilinear motion. Examples of relative motions: Galileo transformations.

2. Mean and instantaneous acceleration. Uniformly accelerated motion. Galileo and the experimental approach. The fall of the grave.

3. Vectors of the plane. Flat angles. Scalar product. Projectile motion and safe zone. Uniform circular motion.

4. First law of dynamics (of inertia). Forces. Second and third principles of dynamics. Weight force and gravitational mass. Momentum.

5. Work for constant forces in one dimension. Kinetic energy for positional forces. Extension to two and three dimensions. Examples of forces with potential

6. Newtonian gravitational force (point mass). Kepler's laws for circular orbits. Work of the gravitational force. Gravitational force of a full homogeneous sphere (Newton's theorem).

7. Systems of material points. The center of gravity. One-dimensional collisions. Rotations. Torque and angular momentum, rotational kinetic energy. The pendulum: law of isochronism in the case of small oscillations.

8. Postulates of Relativity. Lorentz transformations. Minkowski space-time. Length contraction, time dilation. Simultaneity and causality.

9. Relativistic Dynamics. Relativity of Newton's laws. Rest mass and relativistic mass. Equivalence between mass and energy. Relativistic momentum and conservation of the four-momentum. Relativistic collisions.

10. The random walk. Independent steps theory. 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

The assessment includes a written test followed by an oral exam to be taken in the same session.

The written test consists of solving some exercises on the fundamental topics of the course. To be admitted to the oral exam, a minimum passing grade in the written test is required.

The oral exam, which may start with a discussion of the written test, delves into the proofs of the results presented in the course. The final grade, out of thirty, takes into account both the written test and the oral exam results.

Office hours

See the website of Daniele Tantari