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.
Think of the inertia of a bucket of water on a string that you are holding by the string.
If you are standing still the water and bucket and string behave like you expect.
Start running suddenly and the bucket will seem to swing back behind you. Your frame of reference is in motion. But when I watch you do this I see a bucket and water at rest. Their inertia resists the sudden acceleration.
As you pull the string along in your run, the swinging will stop. And with no acceleration (you are in a constant running velocity) the bucket will hang straight down again. The bucket and water are in your moving frame of reference. Their inertia is clear.
What if you stop?
Just like when you started running the inertia of the bucket and water will cause them to continue moving, swinging up. Their inertia is linear, but show up as an arc due to the string you're holding when you accelerate to a stop. The water stays in the bucket because it's geometry tilts its axis, keeping the bottom pointing in the direction of the watet's inertia.
If you were carrying the water on a spoon in the same conditions the water would spill. Because it doesn't tilt the right way to hold it in.
If, at that moment of stopping, you started swinging your arm in a circle you could create a circling bucket from your question. Sometimes the bucket will be upside down, but with sufficient acceleration the water will stay in.
It's the inertia doing the trick. Aided by the geometry of the bucket.