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I agree that the sensation that we call "weight" is generally limited to ones that are directed roughly parallel to our spinal column, or from front to back, if we happen to be lying down, but I suspect that those feeling are more culturally determined than by the physics.
I don't interpret what I feel in a jet aircraft accelerating forwards as
weight as John seems to imply below. I feel pushed back into my chair.
Same with the rotor-ride I feel pushed into the wall--not heavy. However,
if I'm accelerated upwards I do feel heavier, and downwards lighter. So,
maybe I'm misinterpreting what John wrote, but in my experience the
sensation of weight comes from vertical (or nearly so) forces with
different sensations from horizontal forces. I think we might both agree
though that the sensation of weight in a rotating space station IS from the
surface we are standing on pushing us towards the center of rotation.