Throwing a bottle containing pills to the air vertically Suppose I have a bottle of pills and I throw the bottle in the air vertically. I wonder if the pills inside the box also fly up, or do they remain stable at the bottom of the bottle?
I tried this experiment several times and I think the pills remain stable. I took the top of the bottle off and moved the bottle quickly vertically and observed the pills don't go up. But what if I throw it to the air very quickly? Do they still remain stable?
I don't know if my guess is correct and what physics rule is behind that?
 A: Scale that idea up. Substitute people for the pills and an airplane for the pill bottle. Now fly the airplane in a parabolic path just like the pill bottle follows. Like the pills, the people experience 0 g flight. See Reduced-gravity aircraft
In such a flight, people are not stuck to the floor like they are on the ground. The slightest push will make them float in the air. Unlike people, pills have no sense of fun, and do not push themselves off the floor.
A: In a vacuum, the moment the bottle leaves your hand it will be in free-fall, and both the pills and the bottle will be subject to exactly the same acceleration - namely, $9.8\ \text{m/s}^2$ toward the floor.  As a result, they will move together.
On the other hand, in real life there will be a small amount of air resistance which acts on the bottle (because the air in the room is stationary) but not the pills (because the air trapped in the bottle is moving with the same speed as the pills/bottle are when they leave your hand).  As a result, at the moment the bottle leaves your hand the downward acceleration of the bottle will be slightly more than it would be in vacuum, and therefore slightly more than the pills, so the pills will begin to rise very slightly.
Once the pill bottle reaches its apex and begins to fall back down toward the floor, the situation is reversed - the bottle will accelerate toward the floor at slightly less than $9.8\ \text{m/s}^2$ - and the pills will gently fall back down to the bottom.
Finally, depending on the properties of the pills and bottle, this effect might be swamped by friction or adhesion which would act to keep the pills stationary. Experiments would be required to work out what actually happens on a case-by-case basis.
A: Yes, they will remain stable. As you are applying force on the bottle it starts accelerating upward and the bottle's bottom then apply force on the pills and the pills start to accelerate sticking to the bottom of the bottle. You can understand this by a simple experiment, take a coin over your hand and move your hand vertically how fast you move  your hand the coin will stick to your hand(when you are moving it upward).
A: The short answer is that it depends on the normal force between the pills and the bottom of the bottle. From elementary mechanics, we know that the normal force is (up to a factor of mass) the difference between the acceleration of the bottle and gravity.
Therefore, what happens depends on the profile of the throw. If the downward acceleration of the bottle exceeds that of gravity, the normal force will be less than zero and the pills will lose contact with the bottom of the bottle and fly upwards.
