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 and calculus (derivatives and integrals)
 
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, meaning and implications.
Contact forces: constraint forces, dry friction, static and kinetic, viscous friction and limit velocity. Weight. Centripetal force. Elastic force (Hooke's law). Tension. 

Applications: Motion of a point mass on an inclined plane, with and without friction. Simple pendolum and conic pendolum. Springs. Harmonic oscillator and small oscillation approximation.

Inertial and non-inertial reference systems. Definitions, apparent forces. Coordinate transformations and Galileo's transformations. Relative velocity and relative acceleration theorems. Inertial forces: drag forces and Coriolis forces.  

Bonus: inertial forces due to the Earth's rotation.

Work and energy. Definition of work, power, kinetic energy. Theorem of the kinetic energy. Conservative forces and potential energy. Mechanical energy and its conservation. Potential energy of weight and elastic force. Energy in presence of non conservative forces. Energy conservation and internal energy.

Bonus: Definition of stable and unstable equilibrium, motion reversal points.

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.

Dynamics - moments: Moment of a force. Angular momentum for the point mass and for a system of points. Variation of angular momentum and momentum of a force. Momentum conservation and angular momentum conservation. Cardinal equations of dynamics for point mass systems.  

Bonus: system's motions as seen from the center of mass, Koenig's theorems.

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.

Readings/Bibliography

It is strongly advised to adopt one textbook as a reference, to complement the lecture notes.

Suggested (but not mandatory) textbooks:

• G. Vannini, Gettys Fisica 1, Meccanica e termodinamica, Mc Graw Hill Education (with a broad collection of exercises)
  
• S. Focardi, I. Massa, A. Uguzzoni, M. Villa: Fisica Generale - Meccanica e Termodinamica, Casa Editrice Ambrosiana.

It is strongly recommended to adopt one exercise book addressed to the science and engineering school, in addition to the exercises discussed during the lectures.

Other suitable books:

• 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

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. 

Six exams slots are foreseen per academic year, distributed as follows:

• 3 slots in the winter session (December - February)
• 2 slots in the summer session (June - July)
• 1 slot in the autumn session (September)

Written exam

• The written exam consists of a two-hours long test with three exercises and two questions on the theory part of the course.
• The written exam will be held in presence, except for different provisions taken due to the development of the Covid-19 pandemic
• The maximum score of the written exam is 30 points and the exam is passed with 18/30 or more.
• The validity of the score of the written exam is restricted to the given slot.

Oral exam

•  The oral exam, lasting about 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.
• The teacher might, at her own discretion, reserve herself the option to ask for a oral interview, in case the written exam is not fully sufficient or clarifications are needed. 
• The score of the written exam is a starting point for the oral. The final mark can be higher or lower.

 

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