28626 - General Physics T-A (L-Z)

Learning outcomes

Maturing the basic concepts of General Physics (with particular regard to particle mechanics) by the language of mathematical analysis, vector and integral calculus. To learn the scientifical-technical methodology which is necessary to face in quantitative terms the problems of General Physics.

Course contents

Introduction: the scientific method, experiments, laws, models. Physics quantities and measurement, the International System of units.

Basic trigonometry: summary of the basic trigonometry properties and rules.

Basic calculus: derivatives and integrals. Derivatives and integrals of some elementary functions.

Point-mass kinematics in one dimension: velocity and acceleration. Inverse problem of kinematics. Linear uniform motion, linear uniformly accelerated motion. Falling bodies.

Elements of vector calculus: vector and scalar physical quantities. Vector definition and properties, versor. Operations with vectors and their properties: sum, subtraction, scalar and vector product. Definition of a component, Cartesian description of vectors. Derivative of a versor and of a vector.

Kinematics of point mass in space: position, velocity and acceleration vectors. Trajectory and “intrinsic” description of motion, tangent and normal acceleration. Example of motion in two dimensions: parabolic motion, uniform and accelerated circular motion. Angular quantities. Relative motion and Galileo's transformations.

Dynamics of the point mass: definition of force definition and units. Newton's 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. Elastic force. Definition of work, power, kinetic energy. Theorem of the kinetic energy. Conservative forces and potential energy. Mechanical energy and its conservation. Definition of stable and unstable equilibrium, motion reversal points. Potential energy of weight and elastic force. 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: elastic and perfectly inelastic collisions, conservation laws. Special cases of one-dimensional and two-dimensional collisions. Ballistic pendulum. Moment of a force. Angular momentum for the point mass. Variation of angular momentum and momentum of a force.

Dynamics of the rigid body: definition of rigid body. Introduction to the kinematics and rotational dynamics of the rigid body. Degrees of freedom of a system. Rotational kinetic energy of a rigid body and moment of inertia. Angular momentum of a point-mass system. 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 multi-body system. Angular momentum conservation and collisions with rigid bodies constrained to a fixed axis. Fundamentals about static equilibrium for a rigid body.

Oscillations: simple harmonic oscillator (elastic force); torsion pendulum; simple pendulum; rigid-body pendulum.

Readings/Bibliography

Suggested textbooks:

• G. Vannini, Gettys Fisica 1, Meccanica e termodinamica, Mc Graw Hill Education
  
• S. Focardi, I. Massa, A. Uguzzoni, M. Villa: Fisica Generale - Meccanica e Termodinamica, Casa Editrice Ambrosiana.
• R. A. Serway, J. W. Jewett Jt.: Fisica per Scienze ed Ingegneria - Vol. I - Meccanica e termodinamica - EdiSES
• David Halliday, Robert Resnick, Kenneth Krane: Fisica 1 - Quinta edizione, Casa Editrice Ambrosiana
• P. Mazzoldi, M. Nigro, C. Voci: Fisica Vol.1 Meccanica - Termodinamica, EdiSES
• Any exercise book addressed to the science and engineering school, in addition to the exercises developed suring the lectures. 

The ones above have to be considered as suggested textbooks and are not mandatory. However, it is strongly advised to adopt at least one textbook as a reference, to complement the lecture notes.

Teaching methods

The course consists of 60 hours (6CFU) of frontal lectures. Lectures are given mainly from the blackboard and include theory as well as practical applications and exercises. The latter are finalised to the comprehension of the theory and acquisition of the methodology that is necessary to solve physics problems in a quantitative way. 

Assessment methods

The final examination is aimed at verifying the acquisition of the teaching goals, namely the comprehension of the Newtonian Physics basics, and the acquisition of the scientifical-technical methodology which is necessary to face general physics problems in quantitative terms. 

 

The final examination consists of a mandatory written exam and an optional oral colloquium. 

The written exam consists of a two-hours long test with two or three exercises and questions on the theory part of the course. 
The oral exam, lasting 15-20minutes, covers all the topics of the lectures. If the written exam is passed with a mark of 18 (sufficient) or higher, the oral exam is optional. 

 

Variations with respect to the above may occur in the circumstance in which the final examination can be carried out online only. In this case, new instructions will be published on the lecturer's website under "Useful contents" and "News". Any eventual modification to the examination procedure along the year will be communicated in the same way.

Teaching tools

Theory. The theory lectures are normally held at the blackboard. Powerpoint slides can be used in support. 

Exercises. During the course, it is foreseen to hold practical sessions with exercises about the topics discussed in the theory lectures, in which discussions among students or between teacher and student are encouraged. 

The exercises and their solutions are provided to the students online in the "Virtuale" (Virtual learning Environment) website of UniBO.

Office hours

See the website of Francesca Bellini