AIMS AND LEARNING OUTCOMES

1) reach solid understanding of the basic concepts of classical mechanics;

2) develop problem-solving skills in the context of mechanics;

3) acquire the ability to understand and interpret physical phenomena, exploiting both mathematical tools and arguments based on dimensional analysis and order of magnitude approach;

4) understand and recognise the regime of applicability of physical laws.

TEACHING METHODS

All topics are discussed with examples and complemented with problems and exercises.

SYLLABUS/CONTENT

1. Introduction: measurements and units of measurements, physical observables, dimensional analysis and significant digits. Vectors: definitions and operations.
2. Kinematics of a single particle in one dimension. Definition of velocity and acceleration. Examples of 1-D motion: with costant velocity, with constant acceleration and harmonic motion.
3. Kinematics of a single particle in two and three dimensions. Position vector, displacement, velocity and acceleration. Projectile motion and circular motion.
4. Dynamics of a single particle. Force and Newton’s laws. Dynamics without friction: weight, reaction forces, inclined plane, strings and tension. The elastic force.
5. Static and dynamic friction. The drag. Examples of centripetal forces and the pendulum.
6. Relative motion: velocity and acceleration in different frames. Inertial and non-inertial frames. Fictitious forces: centrifugal forces and Coriolis.
7. Work and energy: work / kinetic-energy theorem. Examples: work done by weight, spring, friction. Conservative forces and potential energy. Conservation of mechanical energy.
8. Systems of particles (I): centre of mass, the first equation of dynamics, work and energy for a system of particles. Collisions between particles.
9. Systems of particles (II): moments, the second equation of dynamics, the centre-of-mass frame,  König theorems. Systems with variable mass.
10. Gravity: Newton’s law of gravitation, the Earth gravitational field, escape velocity. The solar system and Kepler’s laws.
11. Proprieties of rigid bodies: definition and degrees of freedom; the motion of a rigid body. Rigid rotation, rotational inertia e the parallel axis theorem. Continuous bodies.
12.  Dynamics of a rigid body: rolling without slipping; precession; conservation laws and collisions between particles and rigid bodies.
13.  Statics: equilibrium between forces and moments; examples. Elastics properties of solids

RECOMMENDED READING/BIBLIOGRAPHY

-Mazzoldi, Nigro, Voci (mechanics)

-Halliday (mechanics)