What is the equivalent of self-inductance in mechanics?

The equivalent of self-inductance in mechanics is inertia. Just as self-inductance measures the ability of a coil to induce an electromotive force in itself due to a change in current, inertia quantifies an object's resistance to changes in its motion. It reflects how much force is needed to change the velocity of an object, analogous to how inductance relates to the change in current in an electrical circuit. Both concepts describe a system's tendency to oppose changes in its state.