Dimensional Analysis Across the Landscape of Physics
Richard W. Robinett · 2024
Abstract Dimensional Analysis Across the Landscape of Physics introduces readers to the powerful concept that almost all physical quantities in science and engineering can be described using only five base dimensions, mass, length, time, charge, and temperature, and combinations thereof. The subtitle, Classic Results, Textbook Examples, and Exploration of Research, then suggests three overlapping goals of the text in demonstrating the power of dimensional analysis methods to solve problems, from textbook to research levels. The historical background of dimensional analysis is reviewed, and famous examples of its use are included for every topic discussed, along with novel research-based applications. It’s shown that problems in the undergraduate Physics curriculum, in the core areas of classical mechanics, electricity and magnetism, thermal physics, and quantum mechanics can be viewed through the lens of matching dimensions to approach the solution of sometimes complex problems. Examples from many Physics (and Physics-adjacent) fields are also included to show the diversity of topics which can be addressed, across the proverbial landscape of physics, highlighting the interconnections among disciplinary areas (in Physics and beyond) Throughout the book, examples from the current and historical research literature are included to illustrate the power of this technique in solving new problems. Each chapter includes several dozen homework problems to allow readers to practice the techniques presented, often extending the reach of topics covered, and research applications explored.