Dimensional Analysis & Scaling Laws

This lecture covers the fundamental physical dimensions, dimensional analysis, and scaling laws in mechanics. It explains how physical laws must respect the dimensions of quantities, leading to dimensionless groups. The instructor discusses the importance of extended dimensional analysis for slender structures, emphasizing the need to consider different length scales. Examples are provided to illustrate the application of dimensional analysis in determining the interdependency of variables in physical systems. The lecture also delves into the reasons behind thin beams bending rather than shearing, and the factors influencing the load-bearing capacity of structures.