This should be a fun one. I would like to discuss the physics of slapping! Yes, slapping! In this episode River Song smacks the Eleventh Doctor pretty hard in the face, so I thought I could take a look at why the Doctor physically responds the way he does.
Take look at how his entire body moves with the force of River's hand. The interesting thing is that it does not seem like his face reacts the way a normal face would when getting slapped.
Take a look at this:
In this case it is apparent that the bones move first and the rest of face (skin tissue and such) is dragged along after. So why does this not seem to occur when River slaps the Doctor?
Logically, this must mean River's slap delivers a much smaller impulse to the Doctors face. River's slap is quicker and quite forceful but because of the very sharp movement of her hand, the time the force is in contact with the Doctor's face is quite small. Since impulse is force times the change in time, this means that the impulse delivered to the Doctor's face would be much smaller so its impact would then be less visible. Also River's female hand is much smaller so the force is acting over a smaller portion of his face.
As to the actual slap, it seems like River's slap is able to actually rotate the Doctor's entire body. The numbers wouldn't match up though. It is true that given the place River slaps the Doctor it would cause his head to rotate since she strikes only one side of the face horizontally. The issue lies in the fact that impulse delivered by the slap that showed no physical/visible effects on the face could not have possibly been big enough to move his entire body.
Of course this is all theoretical, maybe we just don't a good enough angle on how the slap goes down.
So. Over-dramatized? Not accurately visibly represented? Or is the Doctor over reacting to River's slap?
I don't know but I do know something isn't right about this.
(The gifs are from Doctor Who and Mythbusters respectively).