In Star Trek: Into Darkness, there is a scene in which Khan disables the Enterprise' power, forcing it to be caught in Earth's gravity (Ch. 12). During this scene the crew members are seen falling within the ship as it rotates. For example:
While Kirk and Scotty are running to Engineering, they begin to fall as the ship rotates sideways, losing their hold on the guardrail - only to be saved by Chekov. (Star Trek: Into Darkness, 2013, 1:42:30)
My question is: Since the Enterprise is falling toward Earth, shouldn't the ship and her crew be in freefall? And if so, from the ship's frame of reference shouldn't the crew appear to be unaffected by Earth's gravity?
I know that it's only a movie, but the Star Trek franchise has always taken significant care to adhere to scientific fact. They often can explain any seemingly infeasible phenomena with scientific theory assumed to be proven or applied by the 23rd century. I would be slightly disappointed to find that a simple law of physics was overlooked for dramatic effect.