15749 - Mechanics

Learning outcomes

After completing the course , the student has the basic knowledge of Newtonian mechanics of point particles and particle systems.

He/she has learned the use of the vector calculus and is able to apply the general concepts and the basic laws to solve simple problems of kinematic and dynamic.

Course contents

Module 1

- Math complements. a) vector calculus: vectors, vector operations (addition, subtraction, scalar and vector multiplications), properties of vectors, unit vectors; b ) simple derivatives and integrals of one-variable functions; concepts of partial derivatives of multivariable functions.

- Physical quantities: the concept of physical quantities, vector and scalar physical quantities. Dimensional analysis. Standard unit of measurement and sistems of units of measurement ( S.I. ).

- Kinematics in one and more dimensions: a) the position, displacement, velocity and acceleration; b) rotational variables (displacement, velocity and angular acceleration); c) uniformly accelerated motion; d) motion of projectiles; e) uniform circular motion and centripetal acceleration; f) circular motion in polar coordinates; g) Galilean transformations for inertial systems (position, speed, acceleration).

- Dynamics of material point: a) the three laws of Newton for the forces; b) mechanical forces (contact and not); c) spring force; d) static and dynamic friction; e) work of forces; f) Kinetic energy and theorem of live forces; g) conservative and non-conservative forces; h) circulation of a vector field of conservative forces; i) power definition.

- Potential energy for conservative forces. Conservation of mechanical energy for a material point. Equilibrium: stable, unstable and indifferent.

- Systems of particles: a) the center of mass; b) Newton's laws for particle systems; c) momentum; d) conservation of momentum. Internal and external forces to the system of material points and change in internal energy. Conservation of energy.

- Collisions between material bodies.

- Rotational dynamics: a) rotational kinetic energy; b) moment of inertia; c) moment of force; d) Newton's laws for the rotary motion; e) the rotational kinetic energy conservation; f) centripetal force; g) work and power in rotations.
Roto-translational motion and rolling friction.
Angular momentum and conservation of angular momentum: a) inertial axes of rotation; b) the spinner.

- Non-inertial reference systems. a) real and fictitious forces (drag, centrifugal and Coriolis).

- Static. a) Static equilibrium: b) forces of compression and tension; c) elasticity.

- Newton's Gravitation: a) universal gravitation; b) the acceleration of gravity at the Earth's surface; c) gravitational potential energy; d) movement of the planets, and Kepler's laws.

- The harmonic motion: a) simple harmonic motion; b) uniform circular motion; c) pendulums, simple, torsion and physical; d) harmonic damped and forced vibrations (resonance).

- Fluids. a) Density and pressure. b) ideal fluids. c) fluids at rest. d) Stevin's Law. e) Principle of Pascal. f) Archimedes' principle. g) Pipe flow. h) Bernoulli's principle and applications. i) Introduction to real fluids and viscosity.

 

Module 2

Problem solutions on the arguments of Module 1.

Readings/Bibliography

- Focardi, Massa, Uguzzoni, Villa: Fisica Generale (meccanica e termodinamica), C.E.A. Milano

- R. Resnick, D. Halliday, K. Krane: Fisica 1, C.E.A. Milano

- Mazzoldi, Nigro, Voci: Fisica (Volume I), EdiSES Napoli

- Villa, Uguzzoni: Esercizi di Fisica: Meccanica, C.E.A. Milano

Teaching methods

Lectures at the blackboard and solution of problems in the classroom.

Assessment methods

The final test is unique for both the modules. It consists in both a written and an oral parts.

The written part consists in the solution of a problem about mechanics composed of 3 questions. The test has to be completed in a maximum of 2 hours.

The witten test is preliminary to subsequent oral examination of about 30 min. There is no threshold on the minimum score of the written test to access the oral proof. Results of the writtent test will hold for the examination Session.

The final grade is the weighted average of the written and oral tests and in particular the averege will be rigorous if the written test result is < 15/30.

Office hours

See the website of Paolo Capiluppi

See the website of Luigi Guiducci