Vector algebra, Cartesian bases and components. Dot product, vector product, mixed product and double vector product Exercises of operations with vectors

Specific Objectives

Establish the basics of vector algebra that will be used throughout the course. Practicing vector operations and handling vector components

Dedication

Vector of position, trajectory, polar and spherical coordinates. Velocity, arc parameter, acceleration. Tangential and normal accelerations. Solving problem on the position, velocity and acceleration vectors. Uniformly accelerated motion, circular motion, angular velocity vector. Coordinate axis translation. Solving exercises on motion with constant or variable acceleration, circular motion and relative motion. Rope and pulley systems.

Specific Objectives

Learning the quantitative description of the motion of a particle Practice the quantitative description of a particle motion Learning the properties of some simple motions that are useful. Knowing the changes of position, velocity and acceleration in a change of reference system (without rotation) Practice and consolidate the knowledge of some simple motions. Learning the concept of kinematic constraint.

Dedication

Newton's laws. Inertial systems and inertia forces. Gravitational force. Contact forces. Elastic force. Inclined plane problems, circular motion, pulleys. Tension of a rope. Interaction forces between bodies. Dry friction. Solid-fluid friction. Viscosity in a fluid. Introduction to the dimensional analysis. Solving more advanced problems of particle dynamics. Problems with friction.

Specific Objectives

Understanding the foundations of Newtonian Dynamics and knowing some types of force. Getting good insight into the basic concepts of Newtonian Dynamics. Knowing the various friction forces. Consolidate the basic concepts of Newtonian dynamics and apply them to higher level problems.

Dedication

Definition and calculation of the work and the power done by a force and kinetic energy. Kinetic energy theorem. Applications. Conservative forces, potential energy and energy conservation. Central forces. Work and energy application problems.

Specific Objectives

Understanding the concepts of work, kinetic energy and power. Kowing the relationships between them and some applications. Understanding the concepts of conservative force, potential energy and total mechanical energy. Assimilating well the concepts of work and energy and learning their application.

Dedication

Dedication

Rotating coordinate frames. Velocity and acceleration transformation. Centrifugal and Coriolis forces. Perturbation of gravity due to centrifugal force. Effect on the tides. Effects of Coriolis force: cyclones and anticyclones. Projectile deflection. Problems of relative motion of satellites, projectiles and vehicles.

Specific Objectives

Understand the origin of centrifugal and Coriolis forces. Knowing the effects of the rotation of the Earth that are important in Oceanography and Meteorology. Insightful understanding of the effects of the Earth's rotation.

Dedication

Velocity field, acceleration field. Instantaneous center of rotation Problems finding the angular velocity and velocity field from the velocity of some points. Application of the concept of instantaneous center of rotation.

Specific Objectives

Studying rigid bodies as the first case of continuous medium and their velocity field as an example of a vector field. Understanding the possible motions of a rigid solid and the concepts of angular velocity and acceleration. Understanding the basics of 2D motion of rigid bodies.

Dedication

Dynamics of the center of mass, linear momentum, impulse theorem. Percussive forces. Open systems Problems that can be solved by linear momentum balance/conservation. Definition of angular momentum and law of balance. Angular momentum. Kinetic energy and potential energy of a particle system. Applications. Applications of angular momentum and energy for simple particle systems. Satellite orbit problems.

Specific Objectives

Assimilating the basis of the dynamics of particle systems and, in particular, of continuous media. Understanding and knowing how to apply the laws of balance of linear momentum, angular momentum and kinetic energy. Understanding the concept of percussive force Assimilating the concept of linear momentum and learning the application of the law of balance/conservation Understanding angular momentum as a quantity analogous to linear momentum for rotational motion. Knowing the general laws of the motion of a particle system. Understanding the angular momentum concept and its role in the dynamics of rotational motions. Learning how to apply the energy methods to the dynamics of particle systems.Learning how to apply all this knowledge to the case of satellite orbits.

Dedication

Angular momentum, dynamics of 2D rotation and moment of inertia. Kinetic energy and potential energy of a rigid solid. Problems of translation and rotation motion of one or more rigid bodies. Calculation of some moments of inertia. Equilibrium conditions. Problems of Statics and imminent movement. Solid systems. Complement session 26. Problems of statics.

Specific Objectives

Learning the laws of 2D motion of a rigid solid. Knowing how to apply energy analysis to the motion of rigid bodies. Learning to apply the laws of motion of a rigid solid. Learning to calculate moments of inertia Learning to analyze the equilibrium conditions of a rigid body or a system of rigid bodies, and to calculate the forces involved. Same as session 26. Learning to apply the laws of statics to a rigid body or body system.

Dedication