Fundamentals of Mechanics - LEB


Biomedical Engineering

Curricular Unit (UC)

Fundamentals of Mechanics

Mandatory  x
Scientific Area FIS Category  

Course category: B - Basic; C - Core Engineering; E - Specialization; P - Complementary.

Year: 1st Semester: 2nd ECTS: 5.5 Total Hours: 150
Contact Hours T: 45 TP: 15 PL:15 S: OT:3
Professor in charge

 António Jorge Duarte de Castro Silvestre

T - Lectures; TP - Theory and practice; PL - Lab Work; S - Seminar; OT - Tutorial Guidance.

  • Learning outcomes of the curricular unit

    . Know and master the theoretical foundations of Newtonian mechanics and special relativity.

    2. Be able to analyze and model a variety of problems in Newtonian mechanics and special relativity, by applying the above principles.

    3. Be able expeditiously to perform the calculations required for solving the problems described in the preceding item.

  • Syllabus

    1. Kinematics. Position, velocity, acceleration. Straight line motion. Motion in 2D or 3D. Projectile motion. Circular motion. Simple harmonic motion.

    2. Newton’s laws. Torque. Statics. Linear momentum of a particle and its conservation. Impulse of a force. Angular momentum of a particle and its conservation. Work. Work-energy theorem. Conservative and non-conservative forces. Conservation of mechanical energy and of total energy. Power and efficiency.

    3. Linear momentum of an n-particle system (NPS). Collisions. Centre of mass (CM) of an NPS. and its motion. Translational kinetic energy of an NPS. Angular momentum of an NPS and its conservation.

    4. Dynamics of a rigid body. Rigid-body motion. Rotation about a fixed axis. Moment of inertia. Rotational kinetic energy. Rolling motion. Work and power in rotational motion.

    5. Special relativity (SR). Accelerating and inertial frames. Galilean transformations. Lorentz transformations. Linear momentum and energy in SR. Nuclear energy.

  • Demonstration of the syllabus coherence with the curricular unit's objectives

    The syllabus follows the criteria used internationally in similar courses in engineering degrees. Lectures always include several practical examples which promote classroom discussion and easier assimilation of the theory as well as its connection to other courses in the LEB. The exercises proposed in the problem sets (more than 200) allow students, individually or in group, to apply the theoretical concepts to a wide variety of practical situations and thus gain the necessary confidence and skills to use them correctly in many different contexts. This is to impart to students that calculation is an essential ingredient of physics and the ability to obtain numerical results that can be checked by experimental observation underpins the huge success of modern sciences and technologies.


  • Teaching methodologies

    The lectures follow the expository method, always accompanied by practical examples and with extensive use of the white board. Problems classes are designed to clarify difficulties encounterd when solving the problem sets that are expected to have been previously worked out by the students. The course Moodle pages contain extensive study material, past exams  and external links to complementary study material, including videos and virtual experiments (Java applets).


    Assessment for this course is in the form of one written test, taken at the end of semester, and/or a written exam, taken on either of two set dates. Both test and exam are of 2.5 hours duration and cover the entire syllabus.

    The minimum pass grade is 10 (out of a maximum of 20) in all cases.

  • Demonstration of the coherence between the teaching methodologies and the learning outcomes

    Solving a large number of exercises allows students to strengthen their theoretical knowledge through hands-on practice. Real life examples are used to make a connection with the real world and with other courses The aim is also to enhance student participation and motivation.


  • Main Bibliography

    1. A.J. Silvestre, P.I.C. Teixeira, P.I.C., "Mecânica - uma Introdução", Edições Colibri - IPL, 2ª edição, 2014 (referência bibliográfica de base).

    2. P.M. Fishbane, S. Gasiorowicz and S.T. Thornton, "Physics for Scientists and Engineers", Prentice-Hall, 1996.

    3. D. Halliday, R.Resnick, and J. Walker, "Fundamental of Physics", John Wiley & Sons, Inc., 2001.

    4. P. Tipler, "Physics for Scientists and Engineers", W. H. Freeman and Company, 1999.