Physics I 2

The learning objective of the course is to provide a complete knowledge of classical mechanics via the following learning achievements:

• Knowledge of the fundamental laws of classical mechanics in kinematics, the Newton’s laws and the conservation principles.
• Knowledge of the dynamics of rigid bodies, oscillators, and fluid mechanics.
• Solution to problems in Physics related to the topics treated during the course.

In particular the course aims at developing the following skills:

• Knowledge and understanding: to build the fundamental knowledge of mechanics and thermodynamics, and the understanding of their mathematical description.
• Applying knowledge and understanding: To develop and/or improve the ability to identify the key laws in Physics describing phenomena in mechanics or thermodynamics; to correctly apply such laws to solve problems in Physics by appropriate analytical and numerical skills.
• Making judgements: to provide skills for the estimation of the correct order of magnitude of variables in mechanics and thermodynamics.
• Communication skills: to develop and improve presentation skills and learn the language of science.
• Learning skills: to apply mathematical tools and theoretical models to problems in Physics.

The course is worth 6 CFU and will be structured in front lectures (5 CFU) and example classes (1 CFU).

Physical quantities and measure units. The scientific method. Physical quantities and measure units. The International System of Units (SIU). Scientific notation. Dimensionality. Fundamental quantities and derived quantities. Measurement of errors and approximations. Significant figures. Approximation of mathematical functions.

Vector calculus. Scalar quantities and vectors. Invariance and symmetry of systems. Vector calculus: algebra, derivatives and integrals with vectors.

Kinematics. Equations of motion. Linear motion and uniformly accelerated linear motion. Vertical motion. Harmonic oscillator. Damped linear motion. Motion in a plane: velocity and acceleration. Circular and parabolic motion. Motion in the space.

Dynamics of point particles. Newton’s laws. Impulse (step) and momentum. Sum and equilibrium of forces. Examples: weight, friction, viscosity, centripetal force, elastic force and Hook’s law. Inclined plane. Pendulum. Tension. Frames of reference. Relative velocity and acceleration. Inertial frames of reference. Galilean invariance.

Work and energy. Work, power and kinetic energy. Theorem of kinetic energy and examples. Conservative forces and potential energy. Non-conservative forces. Conservation of energy. Force vs potential energy. Angular momentum. Central forces.

Systems of point particles. Systems of n point particles. Internal and external forces. Centre of mass. Conservation of momentum. Conservation of angular momentum. König’s theorem. Kinetic energy theorem.

Rigid body dynamics. Properties of a rigid body. Motion of a rigid body. Continuous distribution of mass, density and position of the body mass. Rigid rotations in three dimensions in an inertial frame of reference. Energy and virtual work of forces. Inertia. Huygens-Steiner’s theorem. Pendulum. Pure rolling. Conservation of energy in the motion of a rigid body. Rolling resistance. Scattering theory.

Oscillators and waves. Differential equation of a harmonic oscillator. Equation of motion and solution for simple harmonic oscillator. Mass-spring system: a simple harmonic oscillator. Energy of a simple harmonic oscillator. Sum of harmonic oscillators in one and two dimensions. Damped and driven harmonic oscillators. Resonance.

Fluid mechanics. Fluids. Pressure. Static equilibrium. Archimede’s principle. Internal friction and ideal fluid’s viscosity. Fluid flow: steady and unsteady flow. Flow rate. Bernoulli’s theorem. Torricelli’s theorem. Pascal’s principle. Laminar vs turbulent flow.

Gravity. Central forces. Kepler’s laws. Newton’s law of universal gravitation. Inertia vs gravitational mass. Gravitational fields and gravitational potential energy.

1. P. Mazzoldi, M. Nigro, C. Voci “Elementi di Fisica” Meccanica e Termodinamica, II edizione, casa editrice EdiSES;
2. D. Halliday, R. Resnick, K. S. Krane “Fisica 1”, Casa editrice Ambrosiana;
3. R. Serwey, J. Jewett “Fisica per Scienze ed Ingegneria”, Vol.I, V Edizione, casa editrice EdiSES;
4. S. Focardi, I. Massa, A. Uguzzoni, M. Villa “Fisica generale - MECCANICA E TERMODINAMICA”, Casa editrice Ambrosiana.

The exam consists of a written test and an optional oral test.

The written test, evaluated in 30/30, proposes exercises and open questions on the topics covered during the course, whose passing determines a final grade.

The oral exam will take place at the request of the student and will consist of a check on all the contents of the course.

There are NO EXEMPTION TESTS or ITINERE TESTS during the course of the PHYSICS I course.

 

WRITTEN EXAMINATION METHOD

The written test is considered PASS if the student achieves a mark greater than or equal to 18/30. Those who pass the written exam have the right to request the oral exam to demonstrate a more in-depth knowledge of the course.

For the written test, there are 2 sessions in the first exam session period, 2 sessions in the second exam session period and 2 sessions in the third exam session period.

There are also 2 sessions reserved for students who are out of course and laggards (paragraphs 5 and 5 bis of the university teaching regulations) during the suspension of teaching activities, generally in the period April / May or November / December.

There are no further exams beyond those approved by the didactic secretariat.

ORAL EXAMINATION METHOD

In case of passing the written test, the student can optionally take the oral test WITHIN and NOT BEYOND the end of the exam session in which he took the written exam, after which the written exam will be CANCELED.

# EXAMPLE: the student passes the written exam of 30.01.2019 or of 20.02.2019 - which are the 2 written Physics 1 sessions foreseen for the I SESSION of exams, then they CAN take the oral exam by the end of the First Session , i.e. WITHIN and NOT LATER THAN 10.03.2019. #

If the oral exam fails, applicants MUST repeat the written exam.

The dates of the oral exam for each SESSION (I, II, III or EXTRAORDINARY) will be communicated at the beginning of the session for each session by means of a notice on the Studium platform as well as communicated at the time of the written exam.

The questions and exercises proposed in the exams refer exclusively to contents proposed during the lessons.

Example.
1. We discuss inertial and non-inertial reference systems, presenting some real examples.
2. Prove Bernoulli's theorem.