I understand that in order for an object to maintain circular motion, its velocity vector must be travelling perpendicular to its position vector and constantly changing inwards, hence an acceleration towards the center of the circle. I know that the acceleration towards the center is typically caused by other forces, like tension on a string, and that these are called centripetal forces I believe? However, objects in circular motion tend to want to be away from the center instead of towards. A bucket of water tied to a string and twirled around in a circle will result in the water staying in the bucket: if the water is exhibiting circular motion, would it not thusly be accelerating inward, and thus escaping the bucket? I’ve heard that it’s a difference of frame of reference, but even looking from out to in, I can’t see how the water would be accelerating inward and yet remain in the bucket without support. Would there not be some force pushing the water into the bucket? And yet, centrifugal force is considered a fictitious force. I don’t understand. I know I understand some level of physics but please explain it like I’m 5 because I can’t seem to actually understand this.
Right - the water has inertia in a straight line (as does the bucket). When they both try to go straight the string prevents it, accelerating them in a new direction. At each moment you look at the circular path the water’s inertia wants to go in a straight line (tangent to the circle). So at each instant it is behaving exactly as if you had been running in a straight line and stopped.
What I meant about the geometry and axial tilt - imagine that instead of a bucket you had a dinner plate with a bucket handle. So the water was all at the level of the top of the bucket rim on a plate. As soon as you stopped the plate would flip and the water would splash off. Likewise, if you had the string connected only to the bottom edges of the bucket rather than its handle, as soon as you stopped the bucket would flip due to the water’s strong inertial force against the side of the bucket. The setup doesn’t tilt the bucket in the right way to keep the water contained and impart the new acceleration upon it.