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MOOC# Physique générale

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Related publications (33)

Related courses (269)

Related concepts (379)

Lectures in this MOOC (64)

PHYS-100: Advanced physics I (mechanics)

La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant l

PHYS-101(f): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr

PHYS-101(a): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr

Kinetic energy

In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.

Oscillation

Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms.

Moment of inertia

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

Mathematical Basics: VectorsMOOC: Physique générale

Covers the fundamental concepts of vectors, including their characteristics and calculation methods.

Mathematical Reminders: TrigonometryMOOC: Physique générale

Covers mathematical reminders on trigonometry, focusing on angles in radians and trigonometric functions.

Mathematical Reminders: Derivatives, Primitives, IntegralsMOOC: Physique générale

Covers mathematical reminders on derivatives, primitives, and integrals, including common functions and Taylor series expansions.

Direct Trihedra in 3DMOOC: Physique générale

Discusses the importance of direct trihedra in three dimensions and how to verify them using the right-hand rule and perspective drawings.

Kinematics: Position, Velocity, Acceleration, TrajectoryMOOC: Physique générale

Covers the fundamental concepts of kinematics, including reference frames, position vectors, velocity, acceleration, and trajectories.

Aluminium is a metal sought in the industry because of its various physical properties. It is produced by an electrolysis reduction process in large cells. In these cells, a large electric current goes through the electrolytic bath and the liquid aluminium. This electric current generates electromagnetic forces that set the bath and the aluminium into motion. Moreover, large quantities of carbon dioxide gas are produced through chemical reactions in the electrolytic bath: the presence of these gases alleviates the density of the liquid bath and changes the dynamics of the flow. Accurate knowledge of this fluid flow is essential to improve the efficiency of the whole process.The purpose of this thesis is to study and approximate the interaction of carbon dioxide with the fluid flow in the aluminium electrolysis process.In the first chapter of this work, a mixture-averaged model is developed for mixtures of gas and liquid. The model is based on the conservation of mass and momentum equations of the two phases, liquid and gas. By combining these equations, a system is established that takes into account the velocity of the liquid-gas mixture, the pressure, the gas velocity and the local gas concentration as unknowns.In the second chapter, a simplified problem is studied theoretically. It is shown that under the assumption that the gas concentration is small, the problem is well-posed. Moreover, we prove a priori error estimates of a finite element approximation of this problem.In the third chapter, we compare this liquid-gas model with a water column reactor experiment. Finally, the last chapter shows that the fluid flow is changed in aluminium electrolysis cells when we take into account the density of the bath reduced by carbon dioxide. These changes are quantified as being of the order of 30% and explain partially the differences between previous models and observations from Rio Tinto Aluminium engineers.

The presence of aerodynamic vortices is widespread in nature. They can be found at small scales near the wing tip of flying insects or at bigger scale in the form of hurricanes, cyclones or even galaxies. They are identified as coherent regions of high vorticity where the flow is locally dominated by rotation over strain. A better comprehension of vortex dynamics has a great potential to increase aerodynamic performances of moving vehicles, such as drones or autonomous underwater vehicles. An accelerated flat plate, a pitching airfoil or a jet flow ejected from a nozzle give rise to the formation of a primary vortex, followed by the shedding of smaller secondary vortices. We experimentally study the growth, timing and trajectory of primary and secondary vortices generated from a rectangular flat plate that is rotated around its centre location in a quiescent fluid. We systematically vary the rotational speed of the plate to get a chord based Reynolds number \Rey that ranges from 800 to 12000. We identify the critical \Rey for the occurrence of secondary vortices to be at 2500. The timing of the formation of the primary vortex is \Rey independent but is affected by the plate's dimensions. The circulation of the primary vortex increases with the angular position $\alpha$ of the plate, until the plate reaches 30°. Increasing the thickness and decreasing the chord lead to a longer growth of the primary vortex. Therefore, the primary vortex reaches a higher dimensionless limit strength. We define a new dimensionless time $T^*$ based on the thickness of the plate to scale the age of the primary vortex. The primary vortex stops growing when $T^* \approx 10$, regardless of the dimensions of the plate. We consider this value to be the vortex formation number of the primary vortex generated from a rotating rectangular flat plate in a Reynolds number range that goes from 800 to 12000. When $\alpha$ > 30°, the circulation released in the flow is entrained into secondary vortices for $\Rey > 2500$. The circulation of all secondary vortices is approximately 4 to 5 times smaller than the circulation of the primary vortex. We present a modified version of the Kaden spiral that accurately predicts the shear layer evolution and the trajectory of primary and secondary vortices during the entire rotation of the plate.We model the timing dynamics of secondary vortices with a power law equation that depends on two distinct parameter: $\chi$ and $\alpha_{0}$.The parameter $\chi$ indicates the relative increase in the time interval between the release of successive secondary vortices.The parameter $\alpha_{0}$ indicates the angular position at which the primary vortex stops growing and pinches-off from the plate.We also observe that the total circulation released in the flow is proportional to $\alpha^{1/3}$, as predicted by the inviscid theory.The combination of the power law equation with the total circulation computed from inviscid theory predict the strength of primary and secondary vortices, based purely on the plate's geometry and kinematics.The strength prediction is confirmed by experimental measurements.In this thesis we provided a valuable insight into the growth, timing and trajectory of primary and secondary vortices generated by a rotating flat plate. Future work should be directed towards more complex object geometries and kinematics, to confirm the validity of the modified Kaden spiral and explore the influence on the formation number.

Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodetic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. The principle of general (or Lorentz) covariance and the mass-shell constraint make it difficult to parametrize physically adequate 4-forces. Here, we propose a solution to this old problem. We apply our framework to several conservative and dissipative forces. In particular, we propose covariant formulations for Hooke???s law and the constant force and compute the drag due to gravitational and hard-sphere collisions in dust, gas, and radiation media. We recover and covariantly extend known forces such as Epstein drag, Chandrasekhar???s dynamical friction, and Poynting-Robertson drag. Variable-mass effects are also considered, namely, Hoyle-Lyttleton accretion and the variable-mass rocket. We conclude with two applications: (1) The free-falling spring, where we find that Hooke???s law corrects the deviation equation by an effective anti???de Sitter tidal force and (2) black hole infall with drag. We numerically compute some trajectories on a Schwarzschild background supporting a dustlike accretion disk.