- Docente: Luigi Guiducci
- Credits: 6
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Engineering Management (cod. 0925)
Learning outcomes
Basic concepts in general physics, with focus on point-mass mechanics, using a mathematical language and vector and differential calculus. Learning scientific and technical methods to quantitatively solve physics problems.
Course contents
Requirements/Prior knowledge
A prior knowledge of basic mathematics is required to attend this course and understand its content: algebra, trigonometry, functions of one variable, derivatives, integrals, simple differential equations. A short summary of mathematical tools used in the course will be given in the first lectures.
Good spoken and written Italian is a necessary pre-requisite: all lectures and tutorials, and all study material will be in Italian.
Contents
Introduction: Introduction to the course. Scientific method. Experiments, laws, models. The physical quantities and their measurement process. The International System of Units (SI). Summary of basic trigonometry. Summary of basic differential calculus: derivatives, integrals.
One-dimensional kinematics: introduction to the point-mass kinematics. Linear motion, velocity and acceleration. Inverse problem. Falling bodies.
Introduction to the vector calculus: Vector and scalar physical quantities. Vector definition and properties. Versor. Vector operations and properties: sum, subtraction, scalar and vector product, scalar product, vector product. Cartesian description of vectors. Vector operations in a Cartesian description. Versor derivative and vector derivative.
Kinematics of point mass: motion in space: position, velocity and acceleration vectors: definition, vector and Cartesian representation. Trajectory and “intrinsic” description of motion, tangent and normal acceleration. Two dimensional motions: motion of a projectile, uniform and accelerated circular motion. Angular quantities. Relative motions and Galileo's transformations.
Dynamics (point mass): Introduction. Force definition and units. Newton dynamics laws. Inertial reference frames. Constraint forces. Weight. Dry friction, static and kinetic. Motion of a point mass on an inclined plane, with and without friction. Centripetal force: circular motion, conical pendulum. Elastic force. Work, power. Kinetic energy and theorem of the kinetic energy. Conservative forces and potential energy. Mechanical energy and its conservation. Energy diagrams, stable and unstable equilibrium, motion reversal points. Potential energy of weight and elastic force. Non-inertial reference frames. Energy in presence of non conservative forces. Energy conservation and internal energy.
Mechanics of point-mass systems: Momentum. Impulse of a force and impulse theorem. Definition of point-mass systems. Centre of mass. Examples of center of mass for continuous bodies. Center of mass motion. Momentum conservation for isolated systems. Collisions: classification, conservation laws. Special cases of one-dimensional collisions. Collisions in two dimensions. Ballistic pendulum. Moment of a force. Angula momentum per a point- mass. Change of angular momentum and momentum of a force.
Introduction to gravitation: Kepler's laws and universal gravitation law. Inertial and gravitational mass. Cavendish experiment. Derivation of Kepler's laws from Newton's laws. Esamples. Kepler's laws as applied to the motion of earth satellites; geostationary orbits; gravitational potential energy; mechanical energy of planets and satellites; escape velocity.
Rigid body mechanics: definition of rigid body and introduction to rotational kinematics and dynamics for rigid systems. Degrees of freedom. Relationship between linear and angular quantities. Rotational kinetic energy for a rigid body and moment of inertia. Angular momentum of a point-mass system and of a rigid body. Huygens-Steiner theorem. Work and power in rotational motion. Work-energy theorem for the rotational motion. Generalization of the work-energy theorem. Mechanical energy for a system of bodies. Angular momentum conservation and collisions with rigid bodies constrained to a fixed axis. Rolling motion without slipping and with slipping. Fundamentals about static equilibrium for a rigid body.
Oscillations: simple harmonic oscillator (elastic force); torsion pendulum; simple pendulum; rigid-body pendulum.
Readings/Bibliography
The textbooks below are proposed, but are not compulsory. Anyway, to use at least one textbook is strongly advised, to complement notes taken during lectures.
Teaching methods
Classroom lectures, with theoretical explanations, practical examples and exercises.
Assessment methods
Achievements will be assessed by means of a final exam. This is based on an analytical assessment of the "expected learning outcomes" described above.
The final exam consists of a written test and an optional oral examination.
The written test has a duration of 2 hours, during which students are required to solve exercises and answer few questions, without using books, notes and any other external help.
Teaching tools
Normally lectures are given at the blackboard, without slides. For this reason, joining lectures, although not mandatory, is very helpful. There will be regular practice sessions, during which students will be left some time to attack problems autonomously, encouraging discussions among students and between students and the teacher on concepts, principles, formulae which are needed to understand and solve the exercises.
Office hours
See the website of Luigi Guiducci