Newton's law states that anything that is in motion will remain in motion unless acted on by an outside force, so the two principles seem to be directly contradictory, at least at first glance. Newton says that an object that is completely isolated, so that it has no external influences on it, will continue to move. Aquinas denies this.
So how does Feser resolve the conflict? Easy! The object in uniform motion is moved along by....
(wait for it)
Yes, angels are necessary to keep a moving object moving. I'm not making this up, he really says it:
So, it is difficult to see how inertial motion, when interpreted as involving real change, could have a physical cause. But as we implied above, even if its lacks a physical cause, there is nothing in the principle of inertia that rules out a metaphysical cause. Indeed, if inertial motion involves real change, then given the principle of motion together with the absence of a physical cause, such a metaphysical cause is necessary.
Of course, that raises the question of what exactly this metaphysical cause is....
If inertial motion involves real change, then, only a metaphysical cause external to the moving object could be the ultimate source. And we already have a model for such a cause in the Aristotelian tradition. For the motions of celestial bodies were in that tradition regarded as unending, just as inertial motion is (barring interference from outside forces) unending; and while this view was associated with a mistaken astronomy, a metaphysical kernel can be extracted from the obsolete scientific husk. Now the causes of celestial motion in this earlier Aristotelian tradition were, of course, intelligent or angelic substances....
Hence the only possible cause of inertial motion—again, at least if it is considered to involve real change—would seem to be a necessarily existing intelligent substance or substances, of the sort the earlier Aristotelian tradition thought moved celestial objects. (Unless it is simply God Himself causing it directly as Unmoved Mover.)
Here Feser is considering inertial motion as "real change." He also considers what happens if you consider inertial motion as a "state" that doesn't involve any real change: no actualization of a potential. Feser seems to be getting confused by the way physicists use the term "state": the "state" of a (classical) object refers to its location and its rate of change (velocity), so by definition it involves change. Ultimately, though, the question of whether inertial motion is or is not "real change" is not a physical question but a metaphysical one. One would think that Feser's Aristotelian-Thomian metaphysics would tell us which it is. That it cannot just shows how useless that metaphysics is.
The idea that angels are responsible for inertial motion raises a whole (heavenly) host of questions. Presumably, an object at rest doesn't need any angelic mover. However, in Newtonian physics, any uniformly moving reference frame can be considered to be at rest (Galilean relativity). If we have two objects in uniform motion relative to each other, which one does the angel need to guide? If we consider object A at rest, then the angel must move B. But if we consider object B at rest, then the angel must move A. What's a poor angel to do?
And how many angels are needed for this heavenly guidance? If an asteroid is being guided by an angel, and suffers an impact that splits it in two, does the angel recruit another angel to guide the second piece? Or can the first angel handle both pieces? What if the asteroid gets shattered into smaller and smaller fragments? Maybe each elementary particle has its own angel? How many angels are needed to guide a fragment the size of a pin? (And do they dance?)
Once again we see the Sophisticated Theologian in action. When the world doesn't work the way you want it to, just invent some invisible, undetectable beings to fill the gap.
I have to thank Prof. Feser for this paper; it shows more clearly than anything I could write what absurdities result when you try to force the world into a pre-conceived metaphysics.