This is a very good question, and an astute observation. As I am not sufficiently trained in engineering and the mathematics required to answer your question, I can only guess. But, it is an educated guess, based upon a discussion with an engineer at Glock. Apparently, the tiny blocking device in the trigger is so light in weight compared to the spring which holds it in place, that the tiny blocking device (in the S&W, the articulating part in the trigger) will not overcome the spring as it does not develop enough inertia. Glock has tested this out of helicopters and still could not overcome the spring on the little blocking tab. Sorry I cannot explain this part better.
You're right that the safety is defeated when there is enough force to overcome the spring that holds the safety in place. Pulling the trigger easily exerts enough force to move the spring but the force caused by m x a may not do so quite so easily, due to the second component of any vector quantity: direction. Acceleration (and any resultant force due to F = m x a) have both magnitude and direction and neither one alone is sufficient to quantify what happens. By designing the safety so that its direction of motion is not collinear with the trigger's direction of motion, you ensure that the acceleration from a single impact on the gun cannot cause simultaneous consequential motion in the two pieces.
Suppose that you drop the gun onto a hard floor so that the acceleration is exactly collinear with the trigger's direction of motion. The trigger will experience force in the direction of its natural motion and if the force is sufficiently large, it will move the trigger bar, perhaps discharging the gun. Now, suppose that the safety moves perpendicular to the trigger's direction of motion (which is roughly correct). The massive acceleration due to the gun hitting the hard floor also induces a force (possibly a large force) in the safety, but since the safety doesn't move that way, it remains in place.
Now, suppose you drop the gun onto a hard floor so that the acceleration is exactly collinear with the safety's direction of motion. The acceleration is so large that the acceleration induces a force sufficient to overcome the safety's spring. This is still likely to be of no consequence because the direction of the acceleration is perpendicular to the trigger's direction of motion, meaning the trigger cannot move in that direction.
This is clever. If you drop the gun so that you could make the trigger discharge the gun, the safety does not move so the trigger's motion is blocked. If you drop the gun so that you could make the safety move, the trigger does not move. Is this foolproof? No. What S&W engineers are trying to do is reduce the probability of a sequence of events creating an unwanted discharge to levels so miniscule that they are "negligible", an engineering term that means "so small you can pretend it doesn't exist." The non-engineering world tends to view safeties in a more binary fashion: "They definitively stop accidental discharge." Well, no. They just reduce the chances to such small levels that they are unlikely to ever happen and if they do, the company can handle the litigation that might come its way.
Since the firing pin block is subject to the same principles, it is conceivable that the gun could be dropped in such a way as to overcome the spring force that holds the block in place. What is the device that acts as a "cross check" for it? Perhaps the sear, which releases the firing pin, and whose direction of motion is not collinear with the firing pin block. (Actually, the sear's type of motion is not similar to that of the firing pin block, being rotational.) And even if there is no "cross check", you can reduce the chances that an impact will dislodge the firing pin block by using a very stiff spring.
I came to this thread via the safety notice for M&P Shields, where the lack of physics and engineering comprehension was creating a suffocating environment. I hope that this explanation helps non-engineers understand why S&W wants every pistol inspected and why they use such strong language by insisting that every pistol in doubt be sent in for repair. The malfunction of the inertia safety greatly reduces the improbability that a single chain of events that start by dropping the gun can create an accidental discharge. As a Shield owner I won't accept the increased risk and I don't think anybody else should either.
Edit: Now that I'm holding my Shield 9 in my hands, I must amend some of what I said above. I stated that the inertia safety moves perpendicular to the motion of the trigger bar.
This is incorrect. The inertia safety in the trigger rotates on the pin that holds it in the trigger. The part of the safety moved by your trigger finger -- the lower part of the articulated trigger -- moves in a direction similar to that of the trigger bar. The part above the pin does not. Because the motion is rotational (not linear) the part above the pin moves in the opposite direction.
Does this mean that dropping the gun in a fashion that could apply a force of sufficient magnitude and direction to discharge the gun by moving the trigger bar is also likely to move the inertia safety? No, it is unlikely. Why? Well, let's divide the safety into parts: the part above the pin about which it rotates, and the part below. Let's assume (incorrectly) that the mass and position above and below the pin is equal, yielding a center of mass exactly on the pin. Given acceleration due to dropping the gun, there will be no torque on the safety so it will not move. Now, let's assume that the mass and position above and below the pin are not equal; instead, let's assume that the mass above is greater and/or its distance from the pin is greater. This actually enhances the safety because it means that any acceleration that would move the trigger will try to move the safety even more toward the "safe" position, or opposite that of the direction in which your trigger finger pulls the pivot. While this is not the orthagonal geometry of which I wrote above, it is equally clever. And then, to further reduce the chances of the safety failing, you stick a spring on the safety that tends to pull the pivot toward the "safe" position. This is doubly clever.
My safety works just fine so my pistol requires no repair. For this I'm glad, and I also enjoy threads of this kind because we get to explore the physics and engineering of these magnificent devices.
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