Relational Mechanics is a new mechanics that replaces Einstein's theories of relativity. It implements Mach's principle quantitatively based on Weber's relational law and the principle of dynamical equilibrium. It explains Newton's bucket experiment as due to gravitational interaction between the water and the distant universe when in relative rotation. The book is intended for physicists, engineers, mathematicians, historians, philosophers of science and students.

One of the goals of this book is to present the basic phenomena of mechanics through simple experiments performed with inexpensive materials. We present the fundamental experiments on falling bodies, equilibrium and oscillations around equilibrium positions. We also show how the theoretical concepts are formed and modified during this process, just as occurred in the formulation of the basic laws of mechanics.

We show how more complex phenomena can be explained and clarified by means of elementary experiments. Playful and curious experiments are also presented. They stimulate creativity, critical thinking and a sense of humour in science. They also relate everyday phenomena to the fundamental laws of physics.

The emphasis is placed on experimental activities. After the experiments we formulate the definitions, concepts, postulates, principles, and laws describing the phenomena. The materials utilized are very simple, easily found at home or in stores, all of them very inexpensive. Even so, we can carry out very precise experiments and construct sensitive scientific equipment. The reader need not depend on any school or research laboratory, as he can build his own equipment and perform all the measurements.

If the experiments presented here are performed in the classroom, each student should ideally perform all the tasks, even when working in a group. Each one should build his own equipment (support, plumb line, lever, etc.), cut out his geometric figures and then take all this personal material home. This procedure is richer in lessons than simple demonstrations of the effects by a teacher. It is essential that all students put their hands to the plough.

The book is also rich in historical information, which gives the context in which some laws were discovered, and also different approaches taken in discovering them. We are careful about in formulating concepts and physical principles. It will be seen, for example, how difficult is to find the correct words to precisely define the center of gravity so that this concept can encompass a whole series of experiments. We distinguish clearly between definitions, postulates, experimental results, and physical laws. We also distinguish explanations from descriptions of phenomena. These aspects illustrate the sociological and human aspects of the formulation of physical laws.

This book is written for students and teachers of science, physics, and mathematics. It can be utilized at High Schools or at Universities, depending on the level at which each aspect is analyzed and explored. It has enough experimental and theoretical material to be employed in all levels of teaching. Each teacher should adapt the contents presented here to his own school environment. It can also be utilized in courses on the history and philosophy of science.

The best way to grasp the contents of the book is to perform the majority of the experiments described here in parallel with the reading. There are many philosophical, theoretical, and mathematical approaches relating to physical science. But physics is essentially an experimental science. It is the combination of all these aspects that make it so fascinating. For this reason we strongly recommend that the experiments presented in the book be repeated and improved. We hope that the reader will have the same pleasure in performing these experiments as we had in developing them.

The Electric Force of a Current analyzes the electric force between a charge and a circuit carrying a steady current when they are at rest relative to one another. It presents experiments and analytical calculations showing the existence of this force, contrary to the statements of many scientists. The force is proportional to the voltage of the battery connected to the resistive circuit. It also includes calculations of the potential and electric field inside and outside resistive conductors carrying steady currents, and the distribution of charges along the surface of the conductors that generate this field. It contains two appendices that discuss the pioneering and revolutionary works of Wilhelm Weber and Gustav Kirchhoff, and a substantial bibliography of modern literature on the topic.

This volume is a substantially complete presentation of the electrodynamics developed by Wilhelm Weber. Weber's force between point charges is explored and thoroughly analysed. Ampère's force between current elements is discussed in connection with modern experiments relating to the Ampère versus Grassmann--Biot--Savart controversy. Ampère's force is a central feature of this work, as Maxwell maintained it should always be in the study of electrodynamics, although it is included in few textbooks on electromagnetism. A detailed study of this force is an outstanding feature of this book. Other topical questions of physics are analysed, such as a potential-dependent inertial mass, Mach's principle and the origin of inertia, action at a distance as opposed to contact actions, etc. No previous knowledge of the subject is required, and all topics are introduced with both their historical backgrounds as well as modern experimental evidence.

This volume will appeal to physicists, mathematicians, electrical and electronic engineers, historians and philosophers of science.

Em 2005 conheci Alberto Gaspar e seu livro Experiˆencias de Ciˆencias para o Ensino Fundamental, com o qual muito aprendi. O mesmo pode ser dito de outras obras suas que conheci depois.

Entre 2004 e 2007 ministrei aulas em cursos de aperfei¸coamento para professores da rede p´ublica do ensino fundamental e m´edio dentro do projeto Teia do Saber da Secretaria de Educa¸c˜ao do Governo do Estado de S˜ao Paulo. Foi um privil´egio muito grande ter sido convidado a atuar neste programa. O apoio que recebi por parte da Secretaria de Educa¸c˜ao e do Grupo Gestor de Projetos Educacionais da UNICAMP, assim como o contato com os alunos que participaram de minhas aulas, foram extremamente enriquecedores para mim. Tamb´em foram muito proveitosas as trocas de experiˆencias com os professores da UNICAMP que participaram deste projeto. Como parte do meu envolvimento neste projeto resolvi ensinar aos professores de ensino fundamental e m´edio aquilo que havia aprendido com o Norberto Ferreira. Com isto retomei aquelas atividades e tive uma motiva¸c˜ao adicional para escrever este livro, no sentido de compartilhar com o maior n´umero poss´ývel de pessoas todas estas coisas.