- Know how to determine the masses and linear moments in a relativistic process.
- Understand the basic phenomenology of the oscillator movement and know how to determine the normal modes in a system with different degrees of freedom.
- Know how to relate deformation with tension in an elastic material in different situations.
- Know in what kind of means a transverse/longitudinal wave spreads.
1. Covariant formulation of restricted relativity: Newton and Maxwell laws and the principle of relativity; Einstein’s postulates; three-dimensional space covariant formulation; tensors in Minkowski space; conservation of the linear momentum tetravector; total inelastic collision; particle with null mass; centre-of-mass system; collision of two particles; some tetravectors in Physics.
2. Small oscillations of many-particle systems: single degree-of-freedom system; multiple degree-of-freedom systems; the double plane pendulum; vibrations of a linear triatomic molecule.
3. Elasticity theory: second order tensor and orthogonal transformations.
3.1- Deformations tensor: unidimensional and three-dimensional deformations, the deformation tensor; incompatibility relations.
3.2- Tension tensor: tension force per unit volume; balance conditions.
3.3- Hooke’s law: work done by tension forces; elastic bodies; Young’s modulus and Poisson’s ration; the tension graphic versus deformation; theory of rupture and tensile strength.
3.4- Applications to elastic and isotropic materials: traction of a bar; tension in a hollow cylindrical tube; torsion of a bar; flexion of a beam.
3.5- Wave propagation in an infinite and homogeneous medium: flow speed; motion equation; linear approximation for solids; wave propagation in infinite isotropic media: waves and P-waves.
4. Constitutive equations for fluids: fluids in balance, Euler equation; fluids with viscosity; Navier-Stokes equation.
Linear Algebra and Analytical Geometry.
General Physics I and II.
Classic Mechanics I.
Generic skills to reach
. Competence in analysis and synthesis; . Competence to solve problems; . Critical thinking; . Competence in autonomous learning; . Competence in applying theoretical knowledge in practice; . Competence in organization and planning; . Competence in oral and written communication; . Competence to communicate with people who are not experts in the field; . Adaptability to new situations; (by decreasing order of importance)
Teaching hours per semester
total of teaching hours
Laboratory or field work
assessment implementation in 20112012 Resolution of problems : 15.0% Laboratorial or field work : 15.0% Exam: 70.0%
Bibliography of reference
BHATIA A. B.; & SINGH, R. N. (1986). Mechanics of Deformable Media. Adam Hilger.
FEYNMAN, R. P.; SANDS, R. B. Leightonm M. (1977). The Feynmann Lectures on Physics. Addison-Wesley. vol. II.
GOLDSTEIN, H. (1980). Classical Mechanics. 2. ed. Addison-Wesley.
MARION, J. B. & THORNTON, S. T. (1995). Classical Dynamics of Particles and Systems. 4. ed. Academic Press.
FRENCH, A. P. (1968). Special Relativity. W. W. Norton.
Presentation of the different topics exemplified by means of practical applications. Mathematical techniques will be introduced whenever necessary, which are needed for the understanding of the themes and resolution of physics problems: tensors in a four-dimensional space.
Acesso ao laboratório para estudar para vários materiais o diagrama 'deformação versus tensão' e o efeito de forças de torção e de flexão.