If a spaceship was pulled toward a sun, would it spin? I was watching a movie. A spaceship was forced into "warp speed". The co-ordinates could not be set. The spaceships trajectory was that of a nearby sun. Forcing the spaceship to power down was the solution. Now out of "warp speed" and with no computer aid (steering etc) the spaceship was seen to be spinning toward the sun trapped in its gravitation field.
My question is, would the spaceship (typically aerodynamically shaped) spin toward the surface? My opinion is no. The spaceship would just fall flat due to the surface area provided at the bottom of the fuselage 
 A: The angular momentum of a massive sun may cause the freely falling spaceship to start spinning in the direction of the sun's angular momentum for an effect of frame dragging. You can take a look at the Kerr metric which describes the behaviour of the spacetime near a massive spinning object. If you're not familiar with general relativity it could be difficult to understand this effect. Anyhow, consider the Frame dragging section in the wikipedia article I pointed to. You can compare this effect with the one of a sea vortex; I guess you've seen sea vortex in many other movies and you know the effect they have on drifting ships. You can compare these two effects to understand the spinning effect of the spaceship towards the (spinning) star.
EDIT: Of course the fictional effect of a spaceship falling on the sun has been made similar to that of an airplane falling down. Typically, say in WWII movies, airplanes fall down for damages in their aerodynamics (such as broken wings and so on). None in a movie would have talked about the  Kerr metric!
A: The only way for a falling object to be made to rotate and translate is if there was a separate force causing this rotation. 
In an atmosphere this is a net force on one side of the craft whose surface area (and therefore drag) is the highest, causing this part of the craft to rotate away from the direction the entire craft is translating. Essentially different parts of the craft have different terminal velocities in different orientations relative to the falling direction, and will rotate in free fall until an equilibrium orientation is achieved.
In the absence of an atmosphere a similar mechanism is tidal force--an apparent unequal gravitational force on different parts of the same object due to a large massive body. The craft has to be extremely huge or long in order to experience tidal forces, as one end of the craft is closer to the planet than the other end. The closer end falls faster, causing the craft to rotate into the vertical direction. If the craft is a perfect sphere it will just cause the closer side to tidally lock in position while it falls--no rotation at all.
So in space, free spinning in free fall is not due to the free fall. 
