Mechanics and Relativity
Code: 100137 ECTS Credits: 6| Degree | Type | Year | Semester |
|---|---|---|---|
| 2500097 Physics | FB | 1 | 1 |
Contact
- Name:
- José Flix Molina
- Email:
- Jose.Flix@uab.cat
Use of Languages
- Principal working language:
- catalan (cat)
- Some groups entirely in English:
- No
- Some groups entirely in Catalan:
- Yes
- Some groups entirely in Spanish:
- No
Teachers
- Emili Bagán Capella
- Car Pérez Dengra
- José Flix Molina
Prerequisites
The course has two parts (about 7 weeks each) clearly differentiated. There are no prerequisites, but for each part the following recommendations are important:
For the mechanics section.
Mathematics: have a good knowledge of elementary algebra, including vector algebra; have elementary knowledge of calculus, in particular, of derivation, and notions of integration.
Physics: have basic knowledge of mechanics. Specifically: kinematics, forces, and Newtonian elementary dynamics.
Others: have good study habits that allow taking the subject up to date.
For the sections of Fluids and Relativity.
Mathematics: Have a good knowledge of basic mathematics. Have agility with elementary algebra.
Physics: have elementary knowledge of Newtonian kinematics and dynamics.
Others: maintain an open attitude and good study habits that allow taking the subject up to date.
Objectives and Contextualisation
Expand knowledge of classical mechanics, essential to understand more advanced subjects. Introduce the student into the world of special relativity, which is an essential part of modern physics.
Help the student to reach the understanding of the fundamental concepts and the formalism of these disciplines. Develop your ability to deal with exercises and problems of an intermediate level and/or that do not fit a specific typology. Develop analytical skills. Prepare the student to deepen and expand knowledge in more advanced subjects.
As a more specific objective in terms of special relativity, training the student in the use of Lorentz transformations to describe events from different reference systems and solve the most common paradoxes of special relativity.
Train the student in the application of the elementary principles of fluid physics.
Competences
- Act with ethical responsibility and respect for fundamental rights and duties, diversity and democratic values.
- Carry out academic work independently using bibliography (especially in English), databases and through collaboration with other professionals
- Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, and before both specialist and general publics
- Develop strategies for analysis, synthesis and communication that allow the concepts of physics to be transmitted in educational and dissemination-based contexts
- Formulate and address physical problems identifying the most relevant principles and using approximations, if necessary, to reach a solution that must be presented, specifying assumptions and approximations
- Know the fundamentals of the main areas of physics and understand them
- Make changes to methods and processes in the area of knowledge in order to provide innovative responses to society's needs and demands.
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Use mathematics to describe the physical world, selecting appropriate tools, building appropriate models, interpreting and comparing results critically with experimentation and observation
- Work independently, have personal initiative and self-organisational skills in achieving results, in planning and in executing a project
Learning Outcomes
- Analyse and interpret the main experiments related to basic physics.
- Analyse certain open questions in contemporary physics and explain them clearly.
- Apply Newton's laws to simple problems of particle dynamics and those of fixed-axis rigid bodies.
- Apply the Bernoulli and Poiseuille equations for fluids.
- Apply the principles of relativistic conservation to shocks and particle decay.
- Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, in front of both specialist and general publics.
- Contrast the sharpness of mathematical results with margins of error in experimental observations.
- Correctly use principles of conservation.
- Describe the Bernoulli and Poiseuille equations for fluids.
- Describe the Lorentz transformations.
- Describe the basic paradoxes of relativistic kinematics.
- Describe the use of the Doppler effect in astronomical measurements.
- Explain the explicit or implicit code of practice of one's own area of knowledge.
- Identify situations in which a change or improvement is needed.
- Identify situations in which conservation principles are useful.
- Interact across diverse areas of basic physics.
- List and describe Newton's laws.
- Make mathematical rigor compatible with approximate physical modelling.
- Outline and resolve the static equilibrium conditions of simple systems.
- Relate the basic concepts of physics with scientific, industrial and everyday subjects.
- Select good variables and carry out correct simplifications.
- Use complex numbers.
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Use differential and integral calculus.
- Use linear transformations and matrix calculus.
- Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
- Carry out academic work independently using bibliography (especially in English), databases and through collaboration with other professionals
Content
Classical mechanics
Kinematics of the point in one, two and three dimensions. Dynamics of the material point: laws of Newton. Systems of inertial and non-inertial references. Relativity of Galileo. Dynamics of particle systems. Linear momentum. Mass center. Conservation of the linear moment. Moment of a force. Angular moment. Static of solids. Work and energy Conservative forces, potential and mechanical energies. Introduction to the dynamics of rigid solids (fixed or parallel rotation axes). Moment of inertia.
Fluid mechanics
Perfect fluids. Pressure and density Bernoulli equation. Applications: static and dynamic of perfect fluids.
Viscous fluids Viscosity. Law of Poiseuille. Fluid circuits.
Special relativity
Introduction. Einstein's Principle of Relativity. Principle of the constancy of the speed of light. Relativistic kinematics: Lorentz transformations; relativistic space-time. Paradoxes, applications and tests of relativistic kinematics. Relativistic Doppler effect. Definition of relativistic linear energy and momentum and conservation principles.
The (important) part of relativistic electrodynamics will look at Electricity and Magnetism. Other complementary parts will be treated in Waves and Optics.
Methodology
Face-to-face activities (supervised)
In the 2020/21 academic year, due to the pandemic situation, the course will combine face-to-face and online teaching.
According to the measures agreed by the Faculty of Science and the Coordination of the Degree in Physics, during the first semester it is expected that each group will receive tuition
in alternate weeks. Mechanisms for virtual teaching and monitoring for the remaining hours will be established.
Depending on the evolution of the pandemic, teaching could become completely virtual.
There will be two hours a week of theoretical classes and one class of (solving) problems. Additionally, eight hours of specialized seminars will be held in which each group will be divided into two subgroups in order to facilitate the interaction between students and instructors who will supervise the activities.
The theory classes will explain the key points of Newtonian relativity and mechanics, as well as the necessary developments to achieve (at a reasonable level) a consistent and well-structured body of doctrine that allows students to study their applications and solve them problems These problems will be solved and discussed in problem classes and specialized seminars.
Non-attendance activities (autonomous)
Students will have the content of theory classes and problems. Apart from the books (see the bibliography), students will have access (through the Virtual Campus) to the content of the theory classes and, as regards the class of problems, will have the statements that will be solved and discussed. Proposals will be proposed for problems whose assessment will weigh up to the mark of the subject.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Activities
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Problem solving classes | 14 | 0.56 | 4, 3, 18, 6, 19, 21, 8, 24, 25 |
| Theory classes | 28 | 1.12 | 4, 3, 12, 9, 11, 10, 17, 16 |
| Type: Supervised | |||
| Specialized seminars | 8 | 0.32 | 1, 5, 4, 3, 18, 7, 12, 9, 11, 10, 17, 15, 19, 20, 16, 21, 8, 24, 25 |
| Type: Autonomous | |||
| Autonomous Learning | 91 | 3.64 | 2, 4, 3, 18, 12, 9, 11, 10, 17, 15, 19, 20, 16, 21, 8, 24, 25 |
Assessment
The evaluations will be made in 3 calls and in each there will be an examination of theoretical issues and problems, and in the first two, in addition, a delivery of problems to solve at home individually or in groups, as indicated. The qualification of these deliveries can be revalidated in a corresponding exam. The agenda of the first call will include the part of Newtonian mechanics and the second the part of relativity and fluids. Each part will count equivalently in the final grade. The subject is considered approved "by partials" when the geometric mean of the notes of each part is higher than 5.0 (out of 10). These notes include the corresponding delivery.
The third and last call (of re-validation) consists of two written exams corresponding to each of the parts of the subject. Only students who have pending one or both parts and those who want to increase a grade should do so. They can only increase the grades (they have no effect if the grades are lower than those obtained in the previous exams). Those students who present themselves to both parts will have to answer only a selection of some questions (as indicated), since they will have the same time as the students who are examined for only one part. The final grade will be the geometric mean of the notes of each part. To participate in the necessary re-validation have been previously submitted to the two exams for evaluation corresponding to each part of the subject. There is no minimum qualification to be able to participate in the re-validation.
Theoretical questions will be brief and will not require complex calculations. They will asses the assimilation of the concepts developed in the classes.
The problems will be longer and will require more complex calculations. They will test the level of comprehension reached by each student, their ability to formulate mathematically the solution of the different sections and also their ability to calculate. These problems will not necessarily be variations of problems solved in the kinds of problems.
Observation. The two parts of the subject are fundamental pillars of the formation of a physicist. A good grade in one of the parts can not compensate for a poor grade in the other. That is why when calculating the global note we use the geometric mean instead of the arithmetic. The geometric mean differs little from the arithmetic when the notes of each part are similar, but it penalizes the situations in which the notes are unbalanced, especially when one of them is very low.
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Delivery of mechanical problems (recoverable int the written mechanical exam) | 10% | 0 | 0 | 1, 3, 18, 6, 13, 27, 15, 14, 19, 23, 20, 16, 21, 26, 8, 24, 25 |
| Delivery of relativity and fluid problems (recoverable in the written exam of relativity and fluid) | 10% | 0 | 0 | 5, 4, 18, 6, 13, 27, 15, 14, 23, 20, 21, 26, 8, 24, 25 |
| Final written exam or re-validation (optional for those who have the two previous exams approved) | up to 100% | 3 | 0.12 | 4, 3, 6, 7, 12, 9, 11, 10, 17, 19, 23, 16, 8, 24 |
| Written exam of mechanics (recoverable in the final written exam) | 40-50% | 3 | 0.12 | 1, 3, 18, 6, 7, 27, 15, 19, 23, 20, 21, 8, 24, 22, 25 |
| Written exam of relativity and fluids (recoverable in the final written exam) | 40-50% | 3 | 0.12 | 2, 5, 4, 6, 12, 9, 11, 10, 27, 23, 21 |
Bibliography
Theory books
M. Alonso i E. J. Finn. Física. Vol 1, Mecánica. Addison Wesley Longman; 1 edición (2000) [https://cataleg.uab.cat/iii/encore/record/C__Rb1023008]
Tipler+Mosca, Física para la ciencia y tecnología, ed. Reverté, 5a (2003) i 6a (2010) edición [https://cataleg.uab.cat/iii/encore/record/C__Rb1616987]
E. Massó, Curs de Relativitat Especial, Manuals de la UAB (1998). Specific for the relativity part [https://cataleg.uab.cat/iii/encore/record/C__Rb1418525]
P. French, Special Relativity, CTC Press (2017) [https://cataleg.uab.cat/iii/encore/record/C__Rb1364971]
Notes of the parts in the VC. Summarized and, therefore, difficult to assimilate if the theory classes have not been followed. They allow for an overview of the subject.
Problems books
Problems in the VC
Tipler+Mosca, Física para la ciencia y tecnología, ed. Reverté, 5a (2003) i 6a (2010) edición [https://cataleg.uab.cat/iii/encore/record/C__Rb1616987]
Software
No specific software will be used.