From workshop tool to physics classroom: using L-squares to explore static equilibrium and stability

Abstract L-squares, or carpenter’s squares, offer a simple and inexpensive system for introducing students to static equilibrium and mechanical stability. We present a hierarchy of theoretical models, ranging from idealised to realistic, that predict the equilibrium angle of the longer arm with respect to the vertical as a function of geometry, including arm thickness and length ratio, assuming identical thickness and mass density for both arms and ideal contact with the support. The analysis uses the principle of virtual work, which provides an alternative to traditional force-based methods. By eliminating the need to explicitly calculate unknown reaction forces, this principle highlights the essential role of geometry and applied forces in equilibrium, thereby promoting conceptual understanding and offering students a clearer insight into the underlying mechanics. These models are validated through accessible experiments using low-cost, 3D-printed or laser-cut L-squares. A simple, classroom-ready experimental setup is described, allowing students to test theoretical predictions by observing how geometry influences stability. This approach provides a hands-on opportunity to confront theory with practice, explore stability thresholds and understand the relationship between idealised models and real systems. The experimental framework can also be adapted to design classroom activities.