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A bucket is rotating in a uniform circular motion. When the bucket is at the topmost point in the loop, the water does not fall. At this point both the tension and gravitational force is acting on the water, then it should be pulled with an even greater force. Then why does the water not fall?

The same question can be asked about a motorcyclist performing a loop de loop. Why does he not fall on the topmost point when both gravity and normal reaction are acting downwards?

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    $\begingroup$ Interestingly, this is almost the same question/answer as "when I throw a rock upwards, why does it not fall the instant I let go?". $\endgroup$ – Mooing Duck Aug 5 at 17:00
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    $\begingroup$ The tension doesn't work on the water; the tension works on the bucket. The water does fall but the bucket falls faster and catches the water. $\endgroup$ – user253751 Aug 6 at 4:33
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It is a common misconception that objects have to move in the direction of the force. This is false; the acceleration points in the direction of the force. This means the change in velocity points in the direction of the force. It is not the velocity that points in the direction of the force.

At the top of the circle the water is definitely pushed down by both gravity and the normal force. However, the velocity of the water at the top of the circle is horizontal. Therefore, the velocity picks up a downward component. This doesn't remove the horizontal component though. The velocity just starts to point down as well as horizontal, and the circle continues. Note that this is also true for the bucket, so the water stays in the bucket.

A similar system you can think of that you are probably familiar with is projectile motion. At the top of the trajectory the force points down, the velocity is horizontal, and the projectile continues on its parabolic path with both horizontal and vertical velocity. The difference between the projectile and the bucket is that the net force is constant for the projectile. The horizontal component of the velocity never changes. For the bucket the net force is always changing so that the motion is circular. The vertical and horizontal components of the velocity are always changing around the circle. The projectile is falling, but the water isn't purely falling. It's also being pushed by the normal force provided by the bucket.

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The water does fall. It just doesn't fall faster than the bucket. By pulling on the bucket, you keep it around the (also falling) water.

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    $\begingroup$ This is it. The water does (try to) fall, just like the moon falls towards the Earth, now and forever. $\endgroup$ – Peter - Reinstate Monica Aug 3 at 12:50
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    $\begingroup$ @PeterA.Schneider Although is this case it's not the same kind of falling. $\endgroup$ – Aaron Stevens Aug 3 at 21:05
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    $\begingroup$ @AaronStevens how so? $\endgroup$ – Eric Duminil Aug 4 at 11:47
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    $\begingroup$ @EricDuminil With the moon gravity is always centripetal. With the water it is not. Also gravity is not the only force acting on the water. The normal force from the bucket pushes on the water as well. And the bucket would have three forces acting on it (gravity, normal force, and tension). So I wouldn't say the water and bucket are necessarily falling, at least not like the moon. $\endgroup$ – Aaron Stevens Aug 4 at 12:24
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    $\begingroup$ @AaronStevens thanks for the explanation. Water and bucket are falling indeed, but not just falling. $\endgroup$ – Eric Duminil Aug 4 at 12:26
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Two reasons:

  1. The bucket is being pulled down faster.
  2. The water has upward inertia from the upswing.

Gravity acting on the water imposes a constant acceleration - $g$ or $9.81\text{ m/s}^2$. The bucket is also accelerated by you pulling it. In addition to acceleration, both objects also have velocity which is altered by these accelerations. If the bucket is moving fast, then as soon as the water loses contact with it it begins to accelerate only with gravity, slower than the bucket. This allows the bucket to catch up.

With the motorcycle it is even simpler. As the motorcycle approaches the top of the loop, it has very some upwards velocity from riding up the wall. At the apex, all that vertical velocity is converted into horizontal and its vertical velocity is very small. At this point gravity begins to act, and increases its downward velocity. However, gravity can only increase that downward velocity so fast. Before gravity can make it start falling, the much larger horizontal velocity allows the motorcycle to reach the downwards sloping part of the curve, which will accelerate it downwards faster. Because of this, gravity will not make the motorcycle lose contact with the loop (assuming the motorcycle is going fast enough).

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    $\begingroup$ Some unconventional terminology is being used here. "The water has upward inertia from the upswing." Inertia doesn't have a direction. "At the apex, all that vertical velocity is converted into horizontal" There is no "conversion of velocity". $\endgroup$ – Aaron Stevens Aug 5 at 4:07
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Water falls from the bucket or not, it depends on the circular motion of the bucket. If the speed of bucket is as much as the centripetal force and centrifugal force become equal or the inertia of water cancels out the effect of the gravitational pull of the earth, then water not fell down. otherwise, it falls.

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