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(I haven't worked with this physics in decades, my terminology might be off)

First year varsity physics: Inertia is a property of mass. It is the amount of force to start an object moving (or change a moving object). The more mass the more the force requires, in direct relation.

Mechanically speaking, how does inertia work?

The force isn't absorbed, accumulating or converter. The result is that there is an equal but opposite force pushing back - as long as the force is equal or below the inertia threshold. What gives mass have this property?

Does weak, strong interaction (Nuclear Force) or quantum physics feature? (1kg of contained gas has the same inertia as 1 kg of lead. Thus the state or density of matter doesn't matter)

PS: Can it be a property of space-time to resist the movement of matter? (Sounds too much like friction...)

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It is the amount of force to start an object moving (or change a moving object).

No, this isn't right. Any (non-zero) net force will cause an object to accelerate - there is no threshold, as implied by this definition.

Inertia is not a quantitative property. You wouldn't say "this object has inertia equal to [$\ldots$]." We observe that when a net force is applied to an object, it accelerates in the direction of that force; in the absence of a net force, its velocity remains constant. This tendency to persist in its present state of motion (read: maintain constant velocity) is what we refer to as inertia.

A quantitative measure of inertia is the object's (inertial) mass. For a given net force, the inertial mass determines how large the resulting acceleration will be. Objects which have large masses don't accelerate much, while objects with small masses would accelerate more (subject to the same force). We say that objects with large masses have more inertia than objects with small masses, because a larger force is required to achieve the same acceleration.

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