When a bucket full of water is rapidly whirled in a vertical circular path, water does not fall out. Why?it is about the circular motion and...

I believe cetrifugal force is what keeps the water in the bottom of the bucket.  In a situation like the one you describe, an outward force away from the center of rotation is developed as the bucket is swung around a central axis.

In some ways, this is considered a form of gravity, such that designs for space stations include the idea of a large living space built in a circle around a central axis, spinning so that there would be an artificial gravity created along the surface of that outer ring.