To give the feeling of gravity, wouldn’t the spin have to steadily accelerate? Once you were moving at the same speed as the spin, would you still have the sense of weight?
If you are rotating around a fixed point at a constant rate, you are constantly accelerating.
Even though the rotational velocity is constant, the direction of motion is constantly changing, and that can only be accomplished through acceleration.
A way of visualizing it is to imagine a clockwise spinning merry-go-round. When you are at the north end of it you are headed due east. When you are at the south end you are headed due west. Some acceleration had to occur to reverse your direction.
No, the inertia of motion would create the centripetal force which would feel just like gravity.
“To give the feeling of gravity, wouldn’t the spin have to steadily accelerate?”
No. The object (in this case, person) does require constant (or at least continuous) acceleration, but the “spin” does not need to accelerate.
Acceleration is change in velocity (not merely speed). So spin IS constant acceleration even when the speed of the spin remains constant. (In this case the change of velocity is in direction rather than speed.)
A person standing on the inner surface of a spinning space ship IS accelerating toward the center of the spin. The speed of the motion is constant, so the person will not “feel” that motion.
That person will, however, feel the pull of artificial gravity away from the axis of rotation due to centrifugal force caused by the inertia of the person’s moving body.