KINEMATICS AND MECHANICS OF POINT SYSTEMS
Basic elements of mathematics and geometry at the secondary school level.
The final exam consists in a written test including:
1) two exercises (12 points each) where the student will be able to show his/her understanding of the problem, his/her ability to identify the physical laws governing the phenomena and his/her capacity to carry out the necessary calculations;
2) two questions concerning topics discussed in class (5 points each) where the student will be able to show his/her comprehension of the nature of the physical laws and their domain of validity.
The final mark is given by the sum of the marks earned in the test. Laude is granted to the student whose final mark exceeds 30.
This course represents the first chance a freshman has to come into contact with the physical laws. Although the main topics addressed in this course, kinematics, dynamics of a point mass and gravitating systems, were already addressed in the secondary school, it is important to give a rigorous, complete and detailed introduction at a professional level, in order to provide a solid methodological basis. The concepts of geometry and calculus required for the mathematical formulation of the physical laws will be introduced by the teacher. The experimental facts supporting the fundamental physical laws will be critically discussed.
At the end of the course the successful student will be able
1) to use in an appropriate way the physical laws to frame physical problems;
2) to use the correct mathematical techniques to solve the equations previously obtained;
3) moreover the student will acquire critical sensibility and scientific method.
1) Introduction. Measuring physical quantities. (2 h)
2) Vectors: sum, scalar product, vector (cross) product. Coordinate systems: Cartesian and polar. Elementary introduction to differential calculus (6 h).
3) Kinematics. Trajectory and the description of motion. Velocity and acceleration. Uniform motion, uniformly accelerated motion, harmonic motion. Uniform circular motion, centripetal acceleration. Tangential and normal acceleration. Reference systems: principle of relativity. Relationship between different reference systems (10 h).
4) Dynamics. First and second laws of dynamics. Third law and momentum conservation. Weight. Rheonomic constraints: inclined plane. Elastic forces: Hooke's law.The pendulum. Tensions. Atwood machine (10 h).
5) Frictional laws and viscous forces. Some example of motion in the presence of friction and viscosity. Fictitious forces (4 h).
6) Impulse-momentum theorem.Variable masses. Kinetic energy, work: work-energy theorem. Conservative forces, potential energy. Conservation of mechanical energy. Angular momentum. Central forces and conservation of angular momentum (10 h).
7) Gravitation. Equivalence principle. Newton's law of gravitation. Measuring G: the Cavendish experiment. Gravitational potential energy.Kepler laws. Center of mass and reduced mass. Gauss theorem. Motion of a point in a gravitational field (10 h).
8) Elastic and inelastic collisions. Dynamics of systems of points: Newton's equations and the definition of torque (4 h).
The course is essentially based on lectures, during which the teacher presents the contents of the course in full detail, including mathematical derivations. At the end of each section, as previously detailed, the tutor will solve and discuss with the students few exercises taken from past exams (12 h). An open source software for the numerical solution of differential equations (OdeFactory) will be presented and used during the lessons, in order to get the students used to this kind of techniques.
The teacher is available for questions by appointment. The teacher e-mail is:
alberto.parola@uninsubria.it