Static Equilibrium and Elasticity (Physics)

Recall cards on the static equilibrium of rigid bodies and on stress, strain, and elasticity. Static equilibrium requires zero linear and zero angular acceleration: the first condition sets the vector sum of external forces to zero (translational equilibrium), and the second sets the sum of external torques about any axis to zero (rotational equilibrium), both at once. For rotation about a fixed z-axis the six scalar equations reduce to three, torque magnitude is r F sin(theta), the pivot may be chosen freely, and weight acts at the center of gravity. Solving equilibrium problems: free-body diagrams with forces at their real points of application, choosing the pivot to cancel an unknown, statically indeterminate cases, and the normal, friction, tension, and hinge forces involved. Stress is force per unit area and strain is the dimensionless fractional deformation; within the linear limit stress = elastic modulus times strain, measured in pascals. Tensile, compressive, bulk, and shear stress and strain define Young's modulus, the bulk modulus, and the shear modulus. Elasticity, the proportionality and elastic limits, Hooke's law, the plastic region, permanent deformation, and the fracture (breaking) stress.