Logo

Mechanics, Waves and Relativity

Code: 107591
Credits: 6
2026/2027
Degree programme Type Course
Physics FB 1

Contact lecturer

Name :
Emili Bagan Capella
Email :
emili.bagan@uab.cat

Teaching staff

Ramón Muñoz Tapia

Group languages

You can consult this information at the end of the document.

Prerequisites

The course is divided into two parts (each lasting approximately seven weeks). There are no formal prerequisites; however, the following background is recommended for each part:

For Mechanics and Waves I:

Mathematics: A good knowledge of trigonometry and elementary algebra, including vector algebra, is recommended. Basic knowledge of calculus, particularly differentiation, as well as introductory notions of integration, is also recommended.

Physics: Basic knowledge of mechanics, especially kinematics, forces, and elementary Newtonian dynamics, is recommended.

Other: Students are expected to maintain an open-minded attitude, question assumptions, and develop good study habits in order to keep up with the course.

For Relativity and Waves II:

Mathematics: A good command of basic mathematics and fluency in elementary algebra are recommended.

Physics: Elementary knowledge of kinematics and Newtonian dynamics is recommended.

Other: Students are expected to maintain an open-minded attitude and solid study habits that allow them to follow the course on a regular basis.

Objectives

To broaden students' knowledge of mechanics and waves, which is essential for understanding more advanced courses. To introduce students to the fundamentals of special relativity, a cornerstone of modern physics. To foster a solid understanding of the fundamental concepts and the mathematical formalism underlying these disciplines. To develop students' ability to solve intermediate-level exercises and problems, including those that do not follow a standard pattern, as well as to strengthen their analytical skills. To prepare students to deepen and expand their knowledge in subsequent courses.

A more specific objective related to special relativity is for students to acquire the ability to use Lorentz transformations to describe events from different reference frames and to resolve the most common paradoxes of the theory. Students are also expected to acquire the ability to apply the fundamental concepts of wave phenomena.


Learning outcomes

  • CM01 (Solve problems in the sciences using the fundamentals of the main areas of physics in a professional context.) Solve problems in the sciences using the fundamentals of the main areas of physics in a professional context.
  • CM02 (Evaluate the principal magnitudes involved in a given basic physical system, manipulating them according to fundamental physical laws to draw conclusions about the predictable behaviour of the system under study.) Evaluate the principal magnitudes involved in a given basic physical system, manipulating them according to fundamental physical laws to draw conclusions about the predictable behaviour of the system under study.
  • KM01 (State Newton's laws and their relationship with the movement of particles and fluids.) State Newton's laws and their relationship with the movement of particles and fluids.
  • KM02 (Describe the elementary paradoxes of relativistic kinematics and Lorentz transformations.) Describe the elementary paradoxes of relativistic kinematics and Lorentz transformations.
  • SM01 (Correctly use scientific language, magnitudes and units associated with fundamental physical concepts.) Correctly use scientific language, magnitudes and units associated with fundamental physical concepts.
  • SM02 (Apply the theory, fundamentals and numerical methods of general physics to the resolution of simple problems and the explanation of experimental phenomena.) Apply the theory, fundamentals and numerical methods of general physics to the resolution of simple problems and the explanation of experimental phenomena.

Contents

1. Classical Mechanics

  • Kinematics of a particle in one, two, and three dimensions.
  • Dynamics of a particle: Newton's laws.
  • Inertial and non-inertial reference frames.
  • Galilean relativity.
  • Dynamics of systems of particles: linear momentum, center of mass, and conservation of linear momentum.
  • Torque and angular momentum.
  • Statics of rigid bodies.
  • Work and energy.
  • Conservative forces, potential energy, and mechanical energy.
  • Introduction to the dynamics of rigid bodies (fixed or parallel axes of rotation).
  • Moment of inertia.


2. Waves

  • Wave motion: propagation velocity, amplitude, and wavefronts.
  • Longitudinal and transverse waves. Polarization.
  • Wave equation. Harmonic waves: characteristics, phase, and phase difference.
  • Energy and intensity associated with a wave.
  • Sound: propagation speed, intensity, decibels, ultrasound, and the operation of the human ear.
  • Doppler effect.
  • Principle of superposition.
  • Interference:
  • Superposition of waves with the same frequency.
  • Superposition of waves with different frequencies.
  • Standing waves.
  • Harmonic analysis and synthesis.


3. Special Relativity


  • Introduction.
  • Einstein's principle of relativity.
  • Principle of the constancy of the speed of light.
  • Relativistic kinematics:
  • Lorentz transformations.
  • Relativistic space-time and space-time diagrams.
  • Paradoxes, applications, and experimental tests of relativistic kinematics.
  • Relativistic Doppler effect and the expansion of the Universe.
  • Relativistic momentum and energy.
  • Conservation laws.
  • Collisions and decays.


The contents listed above are indicative and may be subject to minor adjustments depending on the specific development of each academic year. Likewise, the order in which the topics are listed does not necessarily correspond to the order in which they will be covered in class.

Learning activities and methodology

Title Hours ECTS Learning outcomes
Problem-solving classes 14 0.56 CM01, CM02, SM01, SM02
Focused seminars 8 0.32 CM01, CM02, KM02, SM01, SM02
Lectures 28 1.12 CM01, CM02, KM01, KM02, SM01, SM02
Independent learning 86 3.44 CM01, CM02, KM01, KM02, SM01, SM02

Face-to-face activities (guided and supervised)

The course consists of two hours of lectures and one hour of problem-solving sessions per week.

In addition, eight hours of specialized seminars will be scheduled. During these seminars, each group will be divided into two subgroups in order to facilitate interaction between students and the teaching staff, who will supervise the activities. These activities will be assessed and will account for 10% of the final course grade.

The lectures will present the key concepts of special relativity, mechanics, and wave motion, together with the theoretical developments required to build, at an appropriate level, a coherent and well-structured body of knowledge that enables students to study applications and solve problems. These problems will be solved and discussed during the problem-solving sessions and the specialized seminars.

Non-face-to-face activities (independent study)

Students will have access to the material covered in the lectures and problem-solving sessions. In addition to the recommended textbooks (see the bibliography), they will have access, through the Virtual Campus, to the lecture slides and course notes, as well as to the problem sets that will be solved and discussed in class.

Note: Fifteen minutes of one class session, within the schedule established by the School or the Degree Programme, will be reserved for students to complete the teaching and course evaluation surveys.

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

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Problem set submission for relativity and waves II. 10% 3 0.12 CM01, CM02, KM02, SM01, SM02
Written exam of the second part (the grade can be improved through the final exam) 40% 2 0.08 CM01, CM02, KM02, SM01, SM02
Problem set submission for Mechanics and Waves I 10% 3 0.12 CM01, CM02, KM01, KM02, SM01, SM02
Written examination on the first part (recoverable through the final examination). 40% 2 0.08 CM01, CM02, KM01, SM01, SM02
Final or resit written examination (optional for students wishing to improve their final grade). 100% 4 0.16 CM01, CM02, KM01, KM02, SM01, SM02

The course will be assessed through three examination sessions. Each session will consist of a written examination including both theoretical questions and problems. In addition, during the first two examination periods, problems will be assigned during the seminars. These may be discussed in groups, when indicated, but must be submitted individually.

The first examination will cover Newtonian mechanics and mechanical waves. The second examination will cover special relativity and the remaining topics on waves.

Each part will contribute equally to the final grade. The course will be considered passed through continuous assessment if the geometric mean of the grades for the two parts (including the corresponding problem-set submissions) is at least 5.0 out of 10.

The third examination session (the resit examination) will consist of two written examinations, one for each part of the course. Students who have not passed one or both parts through continuous assessment must take only the corresponding examination(s). Students wishing to improve their grade may also take the resit examination. In this case, the grade obtained in the resit examination will replace the grade for the corresponding part, provided that the examination paper is submitted. The final course grade will then be recalculated as the geometric mean of the grades for the two parts.

To be eligible for the resit examination, students must have taken the corresponding two ordinary examination sessions. In addition, they must have obtained a minimum final grade of 3.5 out of 10. Students whose final grade is below 3.5 will fail the course.

The theoretical questions will be brief and will not require lengthy calculations. They are intended to assess students' conceptual understanding of the material covered in class.

The problems will be longer and will require more substantial calculations. They are intended to assess students' level of understanding, their ability to formulate mathematical solutions, and their computational skills. They will not necessarily be variations of problems solved in class.

Note 1. The two parts of the course are fundamental components of a physicist's education. A high grade in one part should not compensate for a very low grade in the other. For this reason, the geometric mean is used, since it penalizes significant imbalances between the two parts. When the two grades are similar, the difference with respect to the arithmetic mean is practically negligible; however, when they differ substantially, the geometric mean provides a more faithful measure of the overall achievement of the course learning objectives.

Note 2. Any irregularity committed during an assessment activity (including academic fraud, plagiarism, or the improper use of AI, unless such use is explicitly authorized in the course guide) that may lead to a significant alteration of the assessment outcome will result in that assessment activity being graded with a mark of 0. If the course guide establishes that obtaining a minimum grade in that assessment activity is a compulsory requirement for passing the course, or if multiple irregularities are detected in assessment activities of the same course, the final course grade will be 0. Without prejudice to these consequences, the corresponding disciplinary proceedings may also be initiated against the student responsible for such irregularities.



Bibliography

Textbooks

  • M. Alonso and E. J. Finn, Physics. Vol. 1: Mechanics.
  • Addison Wesley Longman, 1st edition (2000).
  • P. Tipler and G. Mosca, Physics for Scientists and Engineers.
  • Reverté, 5th edition (2003) and 6th edition (2010).
  • E. Massó, Course on Special Relativity.
  • UAB Manuals (1998). Specific for the special relativity section.
  • A. P. French, Special Relativity.
  • Reverté (1988), reprinted in 2002.

Problem books and resources

  • Problem set collection available on the Virtual Campus.
  • P. Tipler and G. Mosca, Physics for Scientists and Engineers.
  • Reverté, 5th edition (2003) and 6th edition (2010).

Software

No specific software is required to follow the course.

If any simulation or numerical computation is needed, the course will use Google Colab, a platform that allows programming in Python directly from the browser, without the need to install local software. This tool is free, accessible from any device with an internet connection, and very useful for interactively visualizing results.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan first semester morning-mixed
(PAUL) Classroom practices 1 Catalan/Spanish first semester morning-mixed
(TE) Theory 2 Catalan first semester afternoon
(PAUL) Classroom practices 2 Catalan/Spanish first semester afternoon
(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 afternoon
(SEM) Seminars 22 Catalan/Spanish first semester afternoon