Física Geral

The following basic knowledge is recommended:

• Secondary school physics (10th and 11th grades);
• Differential and Integral Calculus, acquired in the Curricular Unit of Calculus I, of the 1st Semester of the 1st Year of the Degree.

The Curricular Unit (CU) consists of 3 types of classes:

1. Theoretical classes, in which the contents of the CU program are exposed.
2. Problem solving classes, in which exercises are solved by applying the knowledge exposed in the theoretical classes.
3. Laboratory classes, in which experiments are carried out within the scope of the CU syllabus.

Inappropriate behavior that in any way compromises the normal functioning of the class is not permitted, the use of cell phones in any typology of classes, and the use of tablets and computers is not permitted in theoretical and theoretical-practical classes. Students who use, or attempt to use, any of the aforementioned devices, or who in any way disrupt the normal functioning of classes, will be expelled from classes and will be marked as an unjustifiable absence.

This course aims to provide students with knowledge in some areas of physics with particular im-portance in the field of Biomedical Engineering. The afore mentioned knowledge is fundamental to a better understanding of some biological processes as well as the principles of operation of several medical and biomedical instrumentation for measuring biological parameters. Thus, students should acquire skills in the fundamental principles and laws in the different areas of physics taught, learn to apply the acquired knowledge in concrete practical situations, as well as interpret and discuss the physical meaning of numerical expressions and results of laboratory experiments.

1. Vector Calculus
1.1. Scalars and vectors;
1.2. Graphical representation of vectors;
1.3. Bound, sliding and free vectors;
1.4. Graphical operations with free vectors: multiplication by a scalar, addition and subtraction;
1.5. Unit vectors;
1.6. Projection of a vector along an arbitrary direction;
1.7. Cartesian representation of vectors: components of a vector, position vector, module of a vector, directing cosines;
1.8. Analytical operations with vectors: multiplication of a vector by a scalar, addition and subtraction of vectors, dot product, cross product, scalar triple product, and derivative of a vector.

2. Particle kinematics
2.1. Inertial referentials
2.2. Position, velocity and acceleration vectors
2.3. One dimension movement: motion laws
2.4. Circular motion
2.5. Projectiles motion
2.6. Tridimensional motion

3. Particle and rigid bocy dynamics
3.1. Particle momentum
3.2. Momentum conservation
3.3. Newton laws
3.4. Force impulse
3.5. Applied, connection and friction forces
3.6. Particle angular momentum
3.7. Force momentum regarding a point and an axis
3.8. Rigid body momentum
3.9. Moment of inertia
3.10. Rigid body dynamics
3.11. Momentum conservation

4. Work and Energy
4.1. Work done by a force
4.2. Power
4.3. Kinetic energy of a particle and rotational and translational kinetic energy of a rigid body
4.4. Kinetic energy theorem
4.5. Conservative forces: potential energy
4.6. Collisions

5. Particle and rigid body statics
5.1. Particle equilibrium
5.2. Rigid body equilibrium
5.3. Structures equilibrium analysis

6. Force and couple systems
6.1. Couple
6.2. Momentum center
6.3. Force translation
6.4. Force equivalent systems
6.5. Momentum central axis

The assessment consists of three components:

• Four laboratory practical assignments, carried out throughout the semester, each worth 1.00 point, for a total of 4.00 points, with a minimum of 2.00 points;
• Written tests, worth a total of 16 points, with a minimum of 7.00 points;
• A maximum attendance bonus of 1.0 point.

1. Laboratory Practical Assignments

• Students must enrol in groups (two or three students) by the end of the first laboratory class.
• Four practical assignments will be carried out, each worth 1.00 point:
  1. Experimental determination of the acceleration of an object on a frictionless inclined plane, using an air track;
  2. Calibration of a dynamometer and experimental setup of a system of concurrent forces in equilibrium using two masses, a dynamometer, and a graduated scale for measuring angles;
  3. Experimental determination of the acceleration due to gravity using a simple pendulum;
  4. Experimental determination of the moment of inertia of a rotational device, of point masses, and of a cylinder.
• Submission of a pre-report is a necessary condition for being allowed to carry out the laboratory work. (Note: the pre-report is available in the supporting materials on the course page on ISEC’s Moodle.) Questions regarding the laboratory work to be carried out, in particular regarding the preparation of the pre-report, must be clarified in advance and in due time with the instructor responsible for the laboratory classes.

Achieving a minimum of 2.00 points in the laboratory component is a necessary condition to pass the course unit.

Note 1.1: Repeat students who obtained at least 2.00 points in the laboratory component in either of the two previous academic years are exempt from completing the laboratory component. For laboratory grading purposes, the highest grade obtained in those academic years will be considered.

Note 1.2: Students covered by regulations or statutes that explicitly grant exemption from class attendance (such as the Working Student legal regime, set out in Articles 89 to 96 of the Labour Code, approved by Law no. 7/2009 of 12 February), who are unable to attend the laboratory practical classes at the regular timetable, must inform the laboratory instructor by the end of the 2nd week of classes. They must also submit a document issued and signed by the entity for which the student works, proving that the work schedule prevents attendance at the laboratory classes at the regular timetable. Failure to comply with the above deadline and to submit the required document implies that the exceptional assessment described in Note 1.3 will not apply.

Note 1.3: Students covered by Note 1.2 must complete two practical assessments corresponding to two of the four laboratory assignments, on dates to be agreed with the laboratory instructor. These dates may be scheduled up to the day immediately prior to the start of the normal exam period. For these assessments, students must prepare and submit the pre-reports for all four assignments by the deadline set by the laboratory instructor. In each assessment session, the assignment to be carried out will be randomly drawn from the four available, with no repetition of the same assignment. Each of the two assignments will be worth 2.00 points, and each assessment will have the same duration as a laboratory class.

2. Written Tests

The written tests consist entirely of multiple-choice questions, with 5 answer options per question, each worth 1.00 point. Correct answers are awarded 1.00 point, incorrect answers are awarded -0.25 points, and unanswered questions are awarded 0.00 points.

The following general rules apply to the written tests:

• Students may consult a single A4 sheet (two sides), prepared entirely by the student; no formula sheet will be provided by the instructors. This sheet must be handed in together with the test, must be handwritten, and may not contain exercise statements or solved exercises; otherwise, the test will be annulled.
• The use of simple calculators is allowed, as well as scientific and graphical calculators, provided that the latter allow (and have activated) exam mode.
• Students may not have in their possession computers, tablets, mobile phones, so-called smartwatches, glasses with integrated electronic devices, or any other electronic device other than a calculator and a simple watch. Students must ensure that any non-permitted devices are handed to the invigilators before the start of the test.
• Any infringement of the above rules entails the immediate annulment of the written test, formal reporting for disciplinary proceedings due to fraud, and the non-award of a grade for the course unit. (See Article 31 of the Academic Regulations of the 1st Cycle of Studies of IPC – Dispatch no. 9859/2022, of 9 August.)

For the written assessment component, students may choose one of two modalities: A) Continuous Assessment, or B) Final Exam Assessment.

A) Continuous Assessment

Continuous assessment consists of three tests carried out throughout the semester, with no minimum in each test, but with an overall minimum of 7.00 points as the sum of the three test grades, according to the following schedule:

The first test, worth 6 points, covers Chapters 1 (Vector Calculus), 2 (Kinematics), and 3 (Dynamics, only up to Section 3.5, corresponding to Linear Dynamics), and takes place between the 6th and 8th week of classes;

The second test, worth 6 points, covers Chapter 3 (Dynamics, the entire chapter) and Chapter 4 (Work and Energy), and takes place between the 11th and 13th week of classes;

The third test, worth 4 points, covers Chapters 5 (Statics) and 6 (Systems of Forces and Couples), and takes place simultaneously with the Normal Exam.

Note 2.A.1: The grade for each test is the arithmetic sum of the marks obtained, with a minimum of 0.00 points.

Note 2.A.2: To pass through continuous assessment, students must attend at least 80.00% of the possible classes of each of the Theoretical and Theoretical-Practical class types, and at least 70.00% of the scheduled classes of each type. Absences duly justified by the Course Coordinator are not counted as absences, nor as possible classes for the purpose of the 80.00% attendance requirement, but they are counted as scheduled possible classes for the calculation of the 70.00% requirement.

B) Assessment by Final Exam

This consists of the exams provided for in the regulations in force at ISEC, structured in three parts, each with the same structure and weighting as the corresponding test.

Note 2.B.1: The final exam grade is the arithmetic sum of the marks obtained, with a minimum of 0.00 points.

Note 2.B.2: Students who choose continuous assessment may, if they wish, and by providing a written and signed indication on the first page of the exam paper, sit the Normal Exam for the full value of the written component (16 points). In this case, the grades obtained in the 1st and 2nd tests are automatically annulled, and only the exam grade is considered, regardless of whether it is higher, equal to, or lower than the grades obtained in the tests.

Note 2.B.3: Students who choose continuous assessment may, if they wish, and by providing a written and signed indication on the first page of the exam paper, sit the 3rd part of the exam (corresponding to the 3rd test) and one additional part from the remaining two parts. In this case, the grade of the part that is not retaken will be considered without the truncation to 0.00 points described in Note 2.A.1.

Note 2.B.4: To pass through final exam assessment, students must attend at least 70.00% of the possible classes of each of the Theoretical and Theoretical-Practical class types. Absences duly justified by the Course Coordinator are not counted as absences, nor as possible classes for the purpose of the 70.00% attendance requirement.

Note 2.B.5: Students covered by regulations or statutes that explicitly grant exemption from class attendance (such as the Working Student legal regime, Articles 89 to 96 of the Labour Code, approved by Law no. 7/2009 of 12 February), who are unable to attend the theoretical and theoretical-practical classes, are exempt from the attendance requirement for exam assessment. The inability to attend the theoretical and theoretical-practical classes must be communicated by the end of the 2nd week of classes, accompanied by a document issued and signed by the entity for which the student works, proving that the work schedule prevents attendance at the laboratory practical classes at the regular timetable. Failure to comply with the above deadline and to submit the required document implies that the exemption from compulsory attendance will not apply.

3. Attendance Bonus

Students who, in each of the theoretical and theoretical-practical class types, attended:

• At least 75% of the scheduled classes are awarded a 0.50-point bonus in the final grade;
• The full 100% of the scheduled classes are awarded an additional 0.5-point bonus in the final grade.

Final Grade

Students who meet the attendance requirements established above for each assessment modality, as well as the minimum requirements in the laboratory assignments and written tests, will pass if C = E + P + B ≥ 9.50, where E is the written assessment grade (0 to 16 points), P is the laboratory grade (0 to 4 points), and B is the total attendance bonus (0.00, 0.50, or 1.00 points).

Students who do not meet any of the established requirements will receive no grade, and the record will show NRC (Does Not Meet Requirements).

Final Note

Students who invoke the clause in:

• Note 1.2 and nevertheless have regular attendance in classes that overlap with the laboratory classes lose the right to invoke that clause and to be assessed in the laboratory component using the method described in Note 1.3, and therefore also being unable to complete any practical assignments that may already have taken place;
• Note 2.B.5 and nevertheless have regular attendance in classes that overlap with the theoretical and theoretical-practical classes lose the right to invoke that clause, and will instead be subject to the minimum attendance requirement set out in Note 2.B.4.

NAO