A Progression of Static Equilibrium Laboratory Exercises

Although simple architectural structures like bridges, catwalks, cantilevers, and Stonehenge have been integral in human societies for millennia, as have levers and other simple tools, modern students of introductory physics continue to grapple with Newton's conditions for static equilibrium. As formulated in typical introductory physics textbooks,^1–4 these two conditions appear as and where each torque τ is defined as the cross product between the lever arm vector r and the corresponding applied force F, having magnitude, The angle θ here is between the two vectors F and r. In Eq. (1), upward (downward) forces are considered positive (negative). In Eq. (2), counterclockwise (clockwise) torques are considered positive (negative). Equation (1) holds that the vector sum of the external forces acting on an object must be zero to prevent linear accelerations; Eq. (2) states that the vector sum of torques due to external forces about any axis must be zero to prevent angular accelerations. In our view these conditions can be problematic for students because a) the equations contain the unfamiliar summation notation Σ, b) students are uncertain of the role of torques in causing rotations, and c) it is not clear why the sum of torques is zero regardless of the choice of axis. Gianino⁵ describes an experiment using MBL and a force sensor to convey the meaning of torque as applied to a rigid-body lever system without exploring quantitative aspects of the conditions for static equilibrium.