Calculus addresses the very issue you are raising. Thanks to Leibnitz and Newton, we are able to meaningfully talk about things like instantaneous velocity, momentum, and position.
Also, your earlier comment about a non-moving object not having momentum is technically incorrect. It DOES have momentum; it just happens to be zero. Heisenberg is saying that we cannot similtaneously know BOTH the position and momentum of quantum particles to an arbitrary degree of accuracy, even when the object is standing still. It is precisely this constraint that tells us that the electron in a Hydrogen atom cannot continue to shed energy after it is in it's ground state, and spiral into the nucleus. If it could, we'd know both the position of the electron (in the nucleus) and it's momentum (zero) at the same time. In effect, Heisenberg's Principle defines the lowest energy state of the electron in an atom; to go any lower would violate the principle.
It DOES have momentum; it just happens to be zero.
Wouldn't that be potential momentum? I know, I know, definitions. Since you have been so kind perhaps you will explain to be the difference between momentum and inertia. In the real world I thought they were opposites but I have seen inertia used in ways that I would have used momentum.