Mechanics and Relativity
Code: 100137 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| 2500097 Physics | FB | 1 |
Contact
- Name:
- Emili Bagan Capella
- Email:
- emili.bagan@uab.cat
Teachers
- Emili Bagan Capella
- Santiago Llorens Fernandez
- Lindber Ivan Salas Escobar
- Arnau Riera Graells
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
The subject has two sections (about 7 weeks each part). There are no prerequisites, but for each of the sections the following recommendations are important:
For the mechanics section.
Mathematics: have a good knowledge of trigonometry, 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: elementary Newtonian kinematics, forces, and dynamics.
Others: students should maintain an open attitude, question everything, and have good study habits that allow them to keep up with the course.
For the Fluids and Relativity sections.
Mathematics: Have a good knowledge of basic mathematics. Have agility with elementary algebra.
Physics: have basic knowledge of Newtonian kinematics and dynamics.
Others: students should be open-minded and should have good study habits that allow them to keep up with the course.
Objectives and Contextualisation
Expand knowledge of classical mechanics, essential to understand more advanced subjects. Expose students to special relativity, which is an essential part of modern physics.
Help students to undersatnd the fundamental concepts and the formalism of these disciplines. Develop their ability to deal with exercises and problems of an intermediate level and/or that do not fit a specific typology. Develop analytical skills. Prepare students to deepen and expand knowledge in more advanced subjects.
A more specific objective concerning special relativity is training students in the use of Lorentz transformations to describe events from different reference systems and solve the most common paradoxes of special relativity.
Train students 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: Newton's laws. Inertial and non-inertial reference frames. Galilean relativity. Dynamics of particle systems. Linear momentum. Center of mass. Conservation of linear momentum. Moment of a force. Angular momentum. Static of solids. Work and energy Conservative forces, potential and mechanical energies. Introduction to the dynamics of rigid bodies (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) topic relativistic electrodynamics will be taught in the Electricity and Magnetism module. Other complementary parts will be taught in Waves and Optics.
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Problem solving classes | 14 | 0.56 | 3, 4, 6, 8, 18, 19, 21, 24, 25 |
| Theory classes | 28 | 1.12 | 3, 4, 9, 10, 11, 12, 16, 17 |
| Type: Supervised | |||
| Specialized seminars | 8 | 0.32 | 1, 3, 4, 5, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 24, 25 |
| Type: Autonomous | |||
| Autonomous Learning | 92 | 3.68 | 2, 3, 4, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 24, 25 |
Face-to-face activities (directed and supervised)
Two hours per week of theory lectures and one hour of problem-solving classes will be delivered. Additionally, eight hours of specialized seminars will be held, in which each group will be divided into two subgroups to facilitate interaction between students and the instructors who supervise the activities.
In the lectures, the key points of relativity and Newtonian mechanics will be presented and developed to achieve (at a reasonable level) a consistent and well-structured body of doctrine that will allow studying their applications and solving exercises. These exercises will be solved and discussed in problem-solving classes and specialized seminars.
Non-face-to-face activities (autonomous)
Students will be provided with the content of the lectures and problem-solving classes. In addition to the textbooks (see the bibliography), students will have access (through the Virtual Campus) to the content of the lectures and, concerning the problem-solving classes, they will be provided with the statements of the exercises that will be solved and discussed. Homework assigments will be proposed. They can only increase the final grade.
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.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Delivery of mechanical problems (recoverable int the written mechanical exam) | 10% | 0 | 0 | 1, 3, 6, 8, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 27 |
| Delivery of relativity and fluid problems (recoverable in the written exam of relativity and fluid) | 10% | 0 | 0 | 4, 5, 6, 8, 13, 14, 15, 18, 20, 21, 23, 24, 25, 26, 27 |
| Final written exam or re-validation (optional for those who have the two previous exams approved) | up to 100% | 4 | 0.16 | 3, 4, 6, 7, 8, 9, 10, 11, 12, 16, 17, 19, 23, 24 |
| Written exam of mechanics (recoverable in the final written exam) | 40-50% | 2 | 0.08 | 1, 3, 6, 7, 8, 15, 18, 19, 20, 21, 22, 23, 24, 25, 27 |
| Written exam of relativity and fluids (recoverable in the final written exam) | 40-50% | 2 | 0.08 | 2, 4, 5, 6, 9, 10, 11, 12, 21, 23, 27 |
Evaluations will be conducted in three sessions, each including an exam with theoretical questions and problems. In the first two sessions, there will also be a problem set to be completed individually or in groups, as specified. The grade for these assignments can be recovered in the corresponding exam. The syllabus for the first session will cover Newtonian mechanics, and the second will cover relativity and fluids. Each part will count equally towards the final grade. The course is considered passed "by partials" if the geometric mean of the grades for each part is above 5.0 (out of 10). These grades include the corresponding assignment.
The third and final session (make-up) consists of two written tests corresponding to each part of the course. These must be taken by students who have pending one or both parts. The final grade for each part will exclusively be the make-up exam grade. Those who take the exam to improve their grade can only increase it (the make-up exam has no effect if the grades are lower than those obtained in previous sessions). The final grade will be the geometric mean of the grades for each part. To participate in the make-up session, students must have previously attended the two evaluation sessions corresponding to each part of the course. There is a minimum grade requirement of 3.5 in the final grade to be eligible for the make-up session.
The theoretical questions will be brief and will not require complex calculations. They will test the assimilation of concepts developed in class.
The problems will be longer and require more complex calculations. They will assess each student's level of understanding, their ability to mathematically approach various sections, and their calculation skills. These problems will not necessarily be variations of problems solved in problem-solving classes.
Note: Both parts of the course are fundamental pillars of a physicist's training. A good grade in one part cannotcompensate for a deficient grade in the other. This is why we use the geometric mean instead of the arithmetic mean to calculate the overall grade. The geometric mean differs little from the arithmetic mean when the grades for each part are similar but penalizes situations where the grades are unbalanced, especially when one of them is very low.
Single Evaluation: Students who have chosen the single evaluation mode must take a final exam consisting of a theory exam with a series of questions about the course (45%). Then, they must take a problem-solving exam with exercises of similar difficulty to those worked on in class (45%). Once completed, they will submit a problem set that they have previously solved at home (10%). These tests will be conducted on the same day, time, and place as the second partial tests of the continuous evaluation mode.
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] (specifically for special relativity)
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
Statements of exercises and problems of the course, and solutions of selected problems will be provided through Campus Virtual
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.
Language list
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 1 | Catalan/Spanish | first semester | morning-mixed |
| (PAUL) Classroom practices | 2 | Catalan/Spanish | first semester | morning-mixed |
| (SEM) Seminars | 11 | Catalan/Spanish | first semester | morning-mixed |
| (SEM) Seminars | 12 | Catalan/Spanish | first semester | morning-mixed |
| (SEM) Seminars | 21 | Catalan/Spanish | first semester | morning-mixed |
| (SEM) Seminars | 22 | Catalan/Spanish | first semester | morning-mixed |
| (TE) Theory | 1 | Catalan/Spanish | first semester | morning-mixed |
| (TE) Theory | 2 | Catalan/Spanish | first semester | morning-mixed |