Explain why the water remains in the bucket instead of getting the teacher wet.?

Question

A teacher fills a bucket half-way with water and attaches a thin rope to the bucket’s handle. The teacher swings the bucket in a circle above his head. 

Answer 1

If anything has a force acting on it towards the center of a circular path equal to F, and it has a perpendicular constant velocity to that force in the plane of the circle equal to √(F•r/m) where r is the radius of the circular path and m is the mass of that thing, then it will move with a circular motion. Any speed less than that and the water will fall out the bucket. 

Answer 2

Centrifugal force CF = m*g*V^2/r ...or m*g*ω^2*r

Answer 3

swinging the bucket  gives the water velocity  and the  direction change caused by the  rope pulling the bucket down  give the water  acceleration  the  gravity is also pulling down   but the bucket  is being pulled back by the  rope but the water inside the bucket keepts trying to move   striaight  and that is why the  water stays in .. you can see if the teacher holds the bucket over his head the water  drops on him  if the bucket is open downward  because there is no  motion of the water moviing up..

Answer 4

It's called acceleration.

Gravity is one type of acceleration, but this can be overcome by centripetal movement.

Answer 5

Really hard water !

Answer 6

The question is very badly worded.  It is highly ambiguous.  When it says "swings the bucket in a circle above his head", does that mean that the circle is in a vertical plane, with the bucket actually upside down at the top of the circle, as the other two respondents seem to assume ?

OR does it mean that the  bucket is being swung in a HORIZONTAL circle  around the teacher's head?  I lean towards this interpretation.  But the answer is basically the same - CENTRIPETAL force to keep the bucket plus contents moving in a circle, instead of flying off at a tangent.  

Motion in a circle requires a force towards the centre to keep the object, or whatever,  constrained to move in the circle.  This produces the apparent outward force (or centrifugal force in common parlance) which is how artificial gravity is produced, as in a rotating spacecraft - or in a spin dryer.  It is the artificial gravity force which keeps the water in the bucket.

Answer 7

I disagree with the wording of the other two answers.  At the top the water is falling.  But the bucket is being pulled down by the rope.  As long as the bucket is accelerating at a greater rate than the water there is no relative downwards motion.  If you permit the rope to go slack the results can be different and interesting.  The bucket and water execute a parabolic (horizontal) motion drenching my students instead.

Answer 8

If the bucket is swinging fast enough, the water stays in the bucket through centrifugal force.  Which is also what keeps the bucket at the end of the rope, rather than falling when it goes upside-down.

Centrifugal force is related to inertia.  The water and the bucket are moving and want to keep moving in a straight line.  This is an example of Newton's first law, that an object in motion tends to stay in motion unless acted on by an external force.  In this case the external force is the rope.  If the rope broke, the bucket full of water would want to fly off in a straight line, in whichever direction they were going at that instant.

Answer 9

Centrifugal force keeps the water in the bucket. He gets wet when he gets tired.