Whether you have the guts to admit it or not, all of us have tried flipping a water bottle before. For some weird reason that nobody can fully explain, this seemingly pedestrian stunt is incredibly hard for many of us, and that arguably is why the flipping bottle trick even went viral in the first place.
Apparently, it seems so challenging to flip bottles successfully that WikiHow even has a detailed page on "How to Do the Water Bottle Flipping Challenge".
If you have faced immense frustration (and embarrassment) trying to impress your friends by flipping empty drinking bottles instead of throwing them into the recycling bin, Operation Einstein's own bottle flipping addicts are here to help you get better!
According to them, achieving a perfect landing is a combination of having just the right amount of water and a simple but well-rehearsed throwing technique.
And that means it's time to break into our idea bank and understand the physics behind #FlippinGoodFun !
Section 1: Resources
All you really need is similar-sized plastic bottles so that we can compare how the water level in each bottle affects the likelihood of a perfect landing
Of course, if you wanna be more ambitious, feel free to assemble a collection of water bottles so you can compare how different shapes and sizes affect bottle flippin'
Section 2: Flipping the Bottle
According to WikiHow, there are a few key steps to achieving a successful bottle flip ...
Step 1: Fill the bottle with water until it is about 1/3 to 1/4 full
- Adding too much water will not allow enough room for it to move back down to the bottom of the bottle during your flip
- Too little water will cause the bottle to not weigh enough and it will flip too fast
Step 2: Grip the bottle between your fingertips and thumb on its neck near the cap
- Place your fingertips and thumb around the top of the neck of the bottle so that your hand is hovering over, but not touching, the cap
- Grip it tightly so when you flip it, the bottom of the bottle goes up into the air
- Your hand will look like a claw if it’s in the right holding position
Step 3: Flick your wrist up and away from you while gripping the bottle
- Leave the bottom of your bottle on a flat surface
- Grip the bottle tightly in your fingers as you flick your wrist up quickly
- The bottom of the bottle should go up and out in a circular motion away from you
- Avoid moving your arm when flipping the bottle; the movement should be all from your wrist
Step 4: Let go of the bottle when its bottom is in the air
- When your wrist is as high as it can go, the bottom of the bottle should be about halfway up the first half of its flip
- Let go of the bottle at this point so it can continue the circle and flip back down, landing after just 1 clockwise circle
Section 3: A Scientific Investigation
From our experience, the advice from WikiHow makes perfect sense. Achieving a perfect landing is indeed a combination of having just the right amount of water and a simple but well-rehearsed throwing technique. But WHY must we follow this rules so fastidiously?
Rather than providing a quantitative treatment of this problem, let us go through a series of intuitive experiments and logical reasoning to find out why!
Determining the Right Amount of Water
Firstly, let us fill three similar 500ml bottles with varying amounts of water. We recommend one to be empty, one to be full, and one to be approximately ⅓ full (i.e. the ideal amount).
All we need to do is to tip the bottles to illustrate differing stability. The bottle that is ⅓ full will definitely be more stable than an empty or full bottle.
Section 4: Explanation
Basic Concepts: Center of Gravity & Stability
[Note: for the sake of basic explanation, we will refer to the terms Centre of Gravity (CG) and Centre of Mass interchangeably]
For those of you who have volunteered with us previously before COVID-19 hit, you may fondly remember one of the most popular experiments for our small-group sessions: the Balancing Bird station.
In this station, the birds and dragonflies appear like they are going to drop to the ground and shatter their wings, but they somehow retain an impressive ability to balance on very small and narrow surfaces. How is that so?
As station facilitators, we usually begin by introducing the concept of Centre of Gravity. We pass a 15 cm ruler to each child, and ask them to balance it.
Intuitively, all of them will be able to balance the 15 cm ruler at the middle (i.e. at its 7.5 cm mark). Their reasoning is that the weight on both sides is equal, just like how a see-saw balances itself at its middle by having kids sit on both sides.
Using this demonstration, we give a name to a phenomenon they already understand, and call this concept the Centre of Gravity. Often, the kids will visualize this concept as having all the weight of an object act at that point, which is also the point where the object typically balances.
We then explain that the 15 cm ruler represents the thin stick-like body of the dragonfly which is lighter. Next, we place the middle of the 30 cm ruler on one end of the 15 cm ruler. This represents the thicker (and much heavier) wings of the dragonfly.
This two-ruler contraption can now be balanced at the end where the 30 cm ruler is placed, similar to how the CG of the dragonfly is near its mouth.
The full explanation with diagrams is available in our Volunteer Handbook which will be accessible once you sign up as a member of our website by clicking on the Members page in our site menu!
Now that we are able to better understand and visualize this mysterious concept called Centre of Gravity, it is time to introduce another childhood toy that many of us might feel nostalgic about!
This is the Roly-Poly Toy, or what's commonly known in Chinese textbooks as 不倒翁!
If you look at the picture, you can easily see that the base of the toy is much thicker and heavier than the top. This gives the toy a much lower Centre of Gravity which allows it to maintain its famous stability and thus its name.
So let's get back to our original question: why is the partially filled bottle more stable at rest? We can break down the answer into three simple parts.
When the bottle is full/empty, we essentially still balance it at the middle. That's because the distribution of mass is uniform, and its CG is at the middle of the bottle.
However, when the bottle is partially filled, the mass is concentrated towards the bottom of the bottle like the Roly-Poly toy (i.e. lower CG )
The bottle is more stable on a flat surface due to its lower CG. So when the bottle lands after flipping in the air, it will be less likely to fall over!
But we've still only managed to answer the first part of our investigation on why we should fill the bottle until it's about 1/3 full. Let's now try to explain why WikiHow exhorts us to flick the bottle in a circular motion when trying to flip and land it perfectly!
Advanced Concepts: Angular Momentum
As the below infographic from Vox explains, rotating the bottle in a circular motion allows the water inside to "slosh around".
As the light bottle spins, the angular momentum is transferred to the heavier water which slows the bottle's spin. The bottle thus stops spinning after one rotation, and lands squarely on a flat surface due to gravity.
Okay, that was a lot to take in. What does all that actually mean, in simple English that a primary school kid can understand?
Let's first think about objects that move. We all know that some objects move faster, while others move slower. Like how a plane moves faster than a car which in turn moves faster than a bicycle. We use the term speed to describe how fast an object moves. So for our example, a plane has a much faster speed than both a car and a bike.
When we imagine an object moving in our head, we typically think of it as moving in a line. That's because we live in such a fast-paced way where we're obsessed with getting from one point to another in the shortest possible time. And that means moving at the fastest possible speed in a straight line so we don't travel such a far distance.
But an object that is rotating is certainly also moving, We certainly won't call a spinning basketball stationary after all. And we can also describe how fast that rotating object spins. The common-sense term to describe is simply speed of rotation.
But scientists like to sound professional and knowledgeable, so they have sophisticated terms to distinguish speed of movement and speed of rotation. How fast we get from one point to another is called LINEAR speed because we tend to move in a straight line.
But when an object rotates, it tends to move at an angle rather than in a straight line, so we use the term ANGULAR speed to describe how fast it rotates. Hope this distinction makes sense!
Speeding Up and Slowing Down | Back to Bottle Flipping ...
What causes a moving object to suddenly slow down? Well, for objects moving in a straight line, we can easily think of a few possibilities. One intuitive option is friction, where the natural roughness of a surface causes a moving object to lose energy and start slowing down.
Another option could be some form of barrier in the object's path. Let's take a game of Pool for example. In Pool, each player is required to use a cue-stick to hit a white ball, causing it to fly in a straight line at high speeds. The white ball has to be aimed at another color ball that the player wants to hit into the goal.
When the white ball strikes the color ball, the color ball will start to move as the white ball's energy is transferred to it, and the white ball eventually slows to a stop.
This same principle applies not just to other objects moving in a line, but also rotating objects like the plastic bottles that we are so obsessed with flipping!
While an empty bottle is flipping (i.e. rotating) in the air, its angular speed remains roughly constant. That's because it faces little resistance to rotating in the air as it is entirely empty!
This is just like a game of heads and tails, where one throws a spinning coin into the air and tries to predict whether it lands on its head or on its tail. The coin faces little resistance, and keeps spinning as it falls, making it very difficult to predict whether the coin will land heads or tails. And that partly explains why statisticians say there is an equal chance that the coin will land on its head or on its tail!
Similarly, the fact that the empty bottle keeps on rotating while it is falling means that it is nearly impossible to control the bottle's descent. Because of this simple fact, the likelihood that the bottle is at the correct orientation (having its base face downwards) is not very high. It is thus incredibly difficult to get the bottle to land upright no matter how good our wrist-flicking technique is.
The same also applies to the completely full bottle. Because it is full of water, there is no room for the water to slosh around. The CG of the bottle and the water it contains thus remains in its original position in the middle of the bottle, and poses little resistance to the rotation of the bottle.
Like the empty bottle, it is incredibly hard to control the descent of a full water bottle, and the likelihood that the base of the bottle faces downwards is also not high.
How About A Partially Filled Bottle?
All that changes when we attempt to flip a partially filled bottle of water. What happens when we flick the partially filled bottle is that the water inside will slosh around and flow downwards along the length of the bottle due to gravity.
A useful, albeit admittedly flawed, analogy is to think of the water inside the bottle as the colored balls in a game of pool. Like how the white ball is forced to expend its energy to make the colored balls move, the bottle is forced to expend its energy to try to make the water inside rotate along with it. Since the water is much heavier than the empty bottle, the rate of the bottle's rotation slows down.
The bottle’s spin is thus gradually slowed as it completes one rotation (i.e. its angular speed decreases), so it is possible to perfectly time the bottle's spinning such that it stops spinning when it completes one rotation, and consequently lands squarely on its base as it falls downwards due to gravity!
A simple analogy would be that of spinning a lucky draw wheel. If the winning 'slice' is smaller, it is harder to land on it and win a prize.
However, if the ‘slice’ was a lot bigger than the others, there would be a higher chance of landing the prize, since a larger portion of each spin is inside the winning slice!
By flipping a partially filled bottle instead of an empty/full bottle, we increase the "win!" slice of the wheel as we can now control the bottle such that it stops spinning when the water is at the bottom of the bottle and the bottle is upright in the air.
But you will still notice in the diagram above that the win! slice doesn't take up the whole lucky draw wheel because perfecting the instance where the bottle stops spinning at the exact moment that it points upright will still take careful timing, precision, and a whole lot of practice!
Further Extension & Update: Scientific Accuracy & Integrity
As much as we've tried to make this explanation simple yet extensive, we believe it is important to point out that there are still some flaws to our experimental method and explanation.
You will notice that in our explanation, we describe three scenarios: empty, full, and partially full. But we do not actually quantify what is meant by partially full, and how it has been determined that we should ideally fill a bottle up to 1/3 of a capacity.
The science behind that is far too mathematical and complicated, so we will attempt to provide a simple qualitative explanation.
WikiHow recommends 1/3 capacity because they claim that adding too much water will not allow enough room for it to move back down to the bottom of the bottle during your flip, while adding too little water will cause the bottle to not weigh enough and it will flip too fast.
After reading our explanation above, we believe that you can attempt to refine WikiHow's theory to make it more accurate and logical.
Adding too much water (i.e. more than 1/3 capacity) will increase the resistance faced by the bottle as it flips and will cause it to slow down rapidly. The bottle will stop spinning even before it completes one rotation cycle, and it will not be upright when it stops spinning.
As for a bottle with too little water, it will indeed "flip too fast" because the water does not exert enough resistance and the bottle will likely complete more than one rotation cycle. Likewise, there is low likelihood that the bottle will be upright when it stop spinning.
Disclaimer: We acknowledge that we have only provided a simplified explanation of the bottle-flipping phenomenon. That's because the aim of Operation Einstein is to nurture a love for learning outside the classroom in our young beneficiaries rather than conduct some sort of Olympiad training program. If you really want to know more about the science behind #FlippinGoodFun, please check out this post and its accompanying references by Scientific American.
Comments