Cours de Physique I Polycopié rappels des cours, exercices et examens résolus : Mécanique du point matériel
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Date
2024-04-22
Journal Title
Journal ISSN
Volume Title
Publisher
University of M'sila
Abstract
This Physics I course (Reminders of courses and solved exercises: Mechanics of the
material point) is designed for students preparing for an undergraduate degree in the fields of
Material Sciences and Science and Technology. It complies with the official program.
The first chapter is devoted to reminders of vector algebra and dimensional analysis.
Both deal with basic physical quantities that are used in expressing the physical laws. In
addition to the necessary reminders, the objective of this part is to introduce clear definitions
and appropriate notations.
✓ The use of vectors in mechanics is fundamental, enabling the representation of the
speeds and accelerations of the material point, the rotations of solids, the
displacement, the applied forces.
✓ A vector is a mathematical entity that represents an element of a vector space E3
associated with an affine space (point), R3 where a direction, modulus, and point of
application are defined.
The second chapter is dedicated to Kinematics. Its aim is to describe the movements of
material point without being interested in the causes which produce them. It only deals with
movements of material points, that is to say exclusively translations.
✓ From the acceleration vector of a material point, know how to find the speed vector,
the time equations of motion as well as the equation of its trajectory.
✓ Know the expression of the position, speed and acceleration vectors in the different
coordinate systems.
✓ Know the definition of some particular movements covered at the end of the chapter.
✓ The object of the kinematics of the material point is to study its movement over time
independently of the causes producing this movement. This part aims to determine the
kinematic quantities such as the acceleration, speed, position vectors and the time
equation of the trajectory in the frame of a reference chosen by the observer.
The third chapter deals with the dynamics of the material point, within the framework
of Newton's mechanics with its three inseparable laws or principles: the law of inertia, the
fundamental law of dynamics and the law of reciprocal actions. The general laws, called force
laws, are considered to be established for a certain number of interactions with applications
intended for predicting the movements of bodies. The notion of angular momentum of a
particle relative to the origin and that of pseudo-forces are also treated.
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✓ Know how to solve a dynamic problem.
✓ Know how to take stock of the forces applying to a previously defined system.
The fourth chapter concerns the third method of analysis which is that of work and
energy. This approach eliminates the calculation of acceleration by directly relating force,
mass, speed and displacement. At first, the work of a force and the kinetic energy of a particle
are considered. Then, the notions of potential and total energy are outline which will applied
to the principle of energy conservation in various practical situations.
✓ Calculate the work of both variable and invariable forces in any displacement.
✓ Application to the calculation of the work of the force of gravity and the elastic force
whatever the orientation of the chosen axes.
✓ Know how to use the kinetic energy theorem.
✓ Understand how to define potential energy from the concept of conservative force.
✓ Learn to use the concept of mechanical energy.