If you were inside and at the tip of a 100 meter tube shaped ship travelling outside of gravity wells, and at a good speed (not relativistic nor ftl); would you perceive the difference if the ship rotated on its hub head over heals (ie in the direction it was travelling) compared to rotating like a propeller? Rotation rate about 4rpm. I believe effect would mostly be felt if changing height and turning at the same time. But even stationary you would feel the spin.
If the ship is not accelerating or decelerating then you would not notice any difference. With a radius of 50 m and a rotation rate of ~4 rpm, there would be an 'outward' or radial acceleration of about 8m/s or 0.8g.
If it was accelerating or decelerating then you would feel the difference.
If the cylinder was accelerating at rate a along its axis then you would feel an additional acceleration perpendicular to the 'floor' in the direction of the acceleration. Assuming a is small compared with g, the effect would be as if the floor was sloping off in the axial direction. You could probably live with that so long as a was less than around 10% of g.
If the cylinder was accelerating perpendicular to its axis (I believe this is what you mean by head over heels it would be a lot more icky. You would feel an accelerative force that would rotate around in a circle once every 15 seconds. At second zero, you might feel an extra downwards force as if going up in an elevator, at second 7.5 you would feel a similar downwards force. At seconds 3.75 and 11.25 you would feel forwards or backwards accelerations respectively (equivalent to the ground sloping forwards or backwards). Unless a was very small you would get very seasick very quickly. Maybe with time you would develop your 'sea-legs'...
If a was comparable to g (or larger) then either direction would be a problem, but with 'propeller' acceleration you could have sloping floors and live more or less normally (so long as acceleration was constant). With 'head-over-heels' acceleration you would be shaken around so much that any day to day activities would be impractical.
And in comment to your title, this has very little to do with the Coriolis effect.
The Coriolis effect would be significant, at that rotational speed, on motion along the length of the tube. The further out from the center you were in the tube, the faster the speed you would be traveling.
First, though, 'up' and 'down' would not be what you might imagine. If the tube were one long corridor, from one end of the tube to the other, then 'up' would not be towards the center of the tube, and 'down' would not be towards the ends of the tube. 'Up' would be towards the 'ceiling' wall of the tube, and 'down' would be the side of the tube you are 'walking' on, from one end to the other. That is, 'down' would be the floor side of the tube on the opposite direction of rotational travel, and up would be the 'ceiling' side in the direction of rotational travel. But you would also have noticeable motion 'away from' the hub as well, propelling you along the floor of the tube. You would perceptually not be going 'down', you would be sliding 'sideways' along the tube. And gaining speed the further you went from the center hub. You would, however, still be sliding along what you would probably perceive as the 'floor' of the tube. Like going down a very long slide.
Throwing a ball along the length of the tube, towards the center axis of rotation, you would have to throw the ball UP towards the ceiling in order for it to go in a perceptive straight line. And even then, if the tube were long enough, it might never reach the mid-point without bouncing off the walls. In fact, if there was an atmosphere, the ball would most likely end up coming back at you. Especially if it hit the floor.
And throwing the ball from the center out to the rim, well, you would just have to let it go from your hands. It would hit the floor, and roll along the length until it hit the end of the tube.
If you wanted to throw the ball straight up in the air, you would have to aim it towards the center of the tube.
Of course, what is the 'floor' and what is the 'ceiling' of the tube would reverse at the mid-point.
That being said, if the tube is not accelerating or decelerating in the direction of travel, it would make no difference if the tube were rotating like a propeller, or tumbling. The reference frame for 'not rotating' would be the center of the hub, and it would be the point where a ball that is dropped would not go anywhere. You would be in the realm of Newtonian physics, where everything would be going at the same rest speed.
If the tube suddenly started to accelerate in the direction of travel, however, you might want to not be a batter in a baseball game. It would put a whole new definition to 'curve ball'. If the tube were rotating like a propeller, a ball thrown along the tube would be seen to be heading for the walls. If the tube were tumbling, it would seem to be picking up speed along the length of the tube, towards whichever end of the tube was 'away from' the direction of acceleration at that particular moment. At 4 rpm, every 15 seconds it would reverse direction like some spirograph pattern.
So no, tumbling in a tube in the direction of travel would NOT be a good idea, if you were accelerating, and trying to play baseball.