Your third point clarifies some things for me a lot. I seem to have forgotten that acceleration describes a change in direction and/or a change in magnitude of the velocity vector: I recall now in my physics textbooks that objects in non-constant circular motion have a tangential acceleration, and the total acceleration lies somewhere between those, but if the velocity remains constant, then the only acceleration is the centripetal acceleration describing the change in the velocity’s direction.
However, I still have some questions about points one and two. I understand that things in circular motion want to fly out tangentially away from the center, not radially away. Yet, in so far as I can observe, objects do seem to press outwards radially. In the example with the bucket of water, the water sticks to the bottom of the bucket instead of pressing against the side wall. In another example, that of those carnival rides that spin people around in a saucer (gravitron I think it’s called?), the carmival goers tend to stick to the wall of the ride as though they were being flung out radially, instead of rolling along the edge or something else. I guess it’s this disconnect between what I know is correct (objects fly tangentially to their circular paths) and what I observe (objects stick to the wall radially away from the center).
I was with you until this line. I spent some time thinking on it and I think I sort of get what you were talking about? Let me see if I can’t explain it back to you. The water and the bucket both want to keep going linearly, which they can’t because of the string. The bucket arcs around, but the inertia of the water keeps going linearly, causing it to press against the bottom of the bucket. If the bucket continues to be driven in circular motion, it’s this momentum that drives the water against the bottom of the bucket? While the side of the bucket drives the water along the circular path?