Learning outcomes of the course unit
This course gives the fundamental concepts of the classical mechanics. These concepts are integrated with exercises. Teaching is focalised on the fundamental theorems. Particular attention is dedicated to the understanding of the conservation theorems.
A good mathematical proparation at high school level is useful for the study of this course.
Course contents summary
Historical evolution of the scientific thought. Galileo, Newton, Einstein and Planck.
Physical quantities. Measure of a physical quantity. The fundamental unities. The physical quantities and the homogeneity principle. Unities of length, mass and time. Unity systems of measure.
Kinematics of a particle. Observer and coordinate reference system. Motion equations. Velocity and acceleration. Linear and circular motions.
Kinematic of a system of particles. Degrees of freedom of a system of particles. The rigid body. Velocity and acceleration of a point in a rigid body. Translational and rotational motions. The relative motions, law of velocity addition and relation between accelerations observed in inertial and noninertial reference frames.
Space and times in classical mechanics. Limits of classical mechanics. The principle of causality. Forces. Newton’s dynamics and inertial reference systems. The force laws. Newton’s dynamics in a noninertial reference system.
Work done by a force. Work calculation for some significant forces: i.e weight, elastic, gravity and coulomb forces. Work-energy theorem. Conservative forces and potential energy. Non-conservative forces. The conservation of mechanical energy and the principle of energy conservation. The potential energy of a diatomic molecule and its approximation to a spring model. Harmonic and anharmonic oscillations.
The dynamic of a system of particles. Center of mass and its properties. Linear momentum of a particle and of a system of particles. The theorem of the center of mass. Conservation of linear momentum. Torque of a force. Angular momentum of a particle and of a system of particles. The motion equation of the rotational dynamics. Conservation of angular momentum. Kinetic energy and angular momentum of a system of particles. Separation of translational and rotational motions. The kinetic energy and the angular momentum of a rigid body. Moments of inertia. Principal axes. The theorem of parallel axes for the moments of inertia. Dynamic equation of a rigid body rotating around a fixed axis. Dynamic of a wheel. Precession. Equilibrium of a rigid body.
Time dependent forces and the dynamics of collisions. The linear and angular momentum theorems. Elastic and inelastic collisions.
The Newton equation of an harmonic oscillator and its mathematical resolution. The oscillation frequency. Oscillation energy. Damped and driven harmonic oscillator. Oscillation of diatomic molecules.
The gravitation and the Kepler laws.
Fluid dynamic. The Arkimedes and Pascal principles and the Bernoulli equation and their consequences.
D.HALLIDAY, R.RESNICK, K.S.KRANE: « Fisica », Vol. 1, Editrice Ambrosiana, Milano.
C.KITTEL, W.D.KNIGHT, M.A.RUDEMAN: « La Fisica di Berkely »,
Vol. 1- Meccanica, Zanichelli, Bologna.
H.C.OHANIAN: « Fisica », Vol. 1, Zanichelli, Bologna.
M.ALONSO, E.J.FINN: « Elementi di Fisica per l?Università
», Vol. 1, Masson Italia, Milano.
E. HECHT: « Fisica 1», Zanichelli, Bologna.
Teaching adds oral lessons and exemplifying exercises. Students are supplied with lecture notes on some subjects and with a collection of problems useful to study for the written examination. Students can take advantage of the teacher tutoring.
The examination is both written and oral. If the written examination gives a negative results it must be repeated before to take the oral exam. The written examination can be taken in any session of examination. The oral examination can be taken during one year starting from the positive result of the written examination. If the oral examination is negative, the student must repeat the written examination.