Water will climb up the walls of the bucket, from centripetal force
corresponding exactly to the centripetal force of spinning your arms while the universe stood still around you
In both of these cases you mean the centrifugal (“fleeing the center”) force, I think. In the case of the bucket, the centripetal (“seeking the center”) force would be the force exerted by the bucket walls and the water itself on the water, “trying” to push it back to the middle of the bucket. In the case of your arms, the centripetal force would be the force exerted inward by the molecular bonds that keep your arms attached to your body.
Water will climb up the walls of the bucket, from centripetal force
corresponding exactly to the centripetal force of spinning your arms while the universe stood still around you
In both of these cases you mean the centrifugal (“fleeing the center”) force, I think. In the case of the bucket, the centripetal (“seeking the center”) force would be the force exerted by the bucket walls and the water itself on the water, “trying” to push it back to the middle of the bucket. In the case of your arms, the centripetal force would be the force exerted inward by the molecular bonds that keep your arms attached to your body.