Circular Motion: Minimum Speed for Water to Stay in a Spinning Bucket

Everyone knows about the physics experiment where you fill a bucket of water and if you spin it fast enough around your head, the water does not fall out, but why is that?

The simple answer is Centripetal Force, however, the water in the bucket has inertia which is Newton's First Law of Motion and states that an object in motion stays in motion unless acted upon by an unbalanced force.

If there was no bucket, the water would not fall straight down either, rather it would follow the parabolic path of the blue line reason being that when an object is spun in a circle, the object wants to move tangentially from the circle, however the bucket is accelerated into the middle and thus contains the water in the bucket. 

The water does not fall on our heads because it is moving tangentially to the circle faster than it is moving downward due to the force of gravity.



Here is a video of me spinning a bucket to demonstrate that water does not fall out if spun in a circle fast enough.

Here is that same action of spinning a bucket of water, but in slow motion. Notice that the rope is pulled taught as the bucket is spun in a circle.

We know that spinning a bucket of water over our heads fast enough will not spill any water, but what is the minimum speed that the bucket can be swung?

Velocity = ??

Radius (from my shoulder to the bucket) = 40 inches, or about 1.02 meters

Free Body Diagram + Calculations: 

(Note: Tension equals 0 because the rope goes slack when the bucket is spun slow enough for water to spill out)

Therefore, the minimum speed that a bucket full of water must be spun around your head so that no water spills out is 3.1 m/s.