Why are inertial forces useful when analyzing machine components with d’Alembert’s principle?

d’Alembert’s principle is useful for analyzing machine components because it simplifies complex problems in dynamics by reducing them to problems in statics.1

By incorporating an inertial force—a fictitious force defined as the negative product of a body's mass and acceleration ($-ma$)—the principle allows one to treat a moving body as if it were in a state of equilibrium. Because it is generally easier to determine unknown forces on bodies at rest than on those in motion, this approach streamlines the calculation of forces and stress within mechanical systems. For instance, when analyzing a rotating disk, engineers can assume a representative element is in equilibrium by balancing real forces with the outward-acting inertial (centrifugal) force.1