Physique1 : MECANIQUE

This handout has been specifically designed for first-year students in the common core of Sciences and Technologies (ST) and Material Sciences (MS). Its purpose is to provide essential foundations in dimensional analysis, vector calculus, point kinematics, and dynamics of a material point in a Galilean reference frame. These concepts are fundamental for studies in the fields of science and technology.

 

The handout we present to you covers two essential topics in physics: dimensional analysis and vector calculus, as well as point kinematics and dynamics of a material point in a Galilean reference frame.

 

The first part of the handout focuses on dimensional analysis, a fundamental method for studying the relationships between physical quantities. You will discover the basics of dimensional analysis, including its definition and use, as well as the dimensions of the International System of Units. This section will allow you to acquire key skills for formulating and understanding physical laws.

 

Next, you will delve into vector calculus, which is essential for describing physical quantities that have both direction and magnitude. You will learn about scalar and vector quantities, as well as the different graphical representations of vectors. You will also explore fundamental operations on vectors, such as dot product and cross product, and discover their remarkable properties.

 

The second part of the handout is dedicated to point kinematics, which studies the motion of objects without considering the forces causing them. You will be introduced to the basic concepts of kinematics, such as the positioning of a material point in space and time, coordinate systems, velocity and acceleration vectors, as well as the Frenet frame to describe curved motions.

 

Moreover, you will explore kinematics with a change of reference frame, where you will study the relative and absolute motions between different frames of reference. You will learn how to describe motions using derivations in a moving frame and understand methods for composing velocities and accelerations.

 

Finally, the third part of the handout addresses the dynamics of a material point in a Galilean reference frame. You will examine the fundamental principles of dynamics, including the principle of inertia, the action-reaction principle, and the fundamental relation of dynamics. You will also understand the concept of angular momentum and its important properties. Additionally, you will explore different forms of energy (kinetic, potential, and mechanical) and their relationship to work and conservative forces.

 

The handout is accompanied by a series of exercises to allow you to practice the presented concepts and methods. Detailed solutions are also provided to assist you in your learning.

 

We hope that this handout will provide you with a solid understanding of dimensional analysis, vector calculus, point kinematics, and dynamics of a material point in a Galilean reference frame. This knowledge is essential for studying physics and comprehending the natural phenomena that surround us. Enjoy reading and happy learning!