Here's a great initiative explanation from Daniel Walsh: kzfaq.info/get/bejne/asuiZcWmrrSsdmQ.html The sponsor is Incogni: : the first 100 people to use code SCIENCE at the link below will get 60% off: incogni.com/science

I have been conducting a version of this experiment for years, I can confirm that it’s impossible to get a golf ball to do anything you want it to do.

Motion amplification on Musical instruments might be very interesting, to see the resonacne of the notes in the body of the instrument. to see what parts of a violin, piano or guitar move, also maybe for a flute or xylophone or something like a trumpet..

There was a thing I saw where a camera focused on a bag of chips through a window could measure the vibrations that speech made on the bag in order to reconstruct voices inside the room the bag was in. I’d love to see that sort of thing amplified.

I work on violins and bows and I would love to see motion amplification of a violin back and compare it with different shaped violins, to see if you can tell them apart visually as well as aurally. Maybe you could also test bows by sending a pulse down one and watching it resonate. You could compare different wood types and structures as well as densities and thicknesses.

If you use spheres coloured in yin-yang style (each hemisphere and its pole with contrasting colours), it may be possible to see if the axis of rotation stays consistent in the entire action on the slo-mo camera.

YES I HAVE AN IDEA! The motion amplification camera video was one of the most interesting so far, and it really jogged my brain. I would love to see which parts of an acoustic guitar vibrate the most when played. The entire body is a soundbox, but certain parts vibrate more than others, leading to differing ideas of how guitars should be braced internally to strike the balance between stability and resonance. In my experience with feeling the body while playing, the area around the bridge (understandably) feels like it resonates the most, whereas the areas surrounding the sound hole seem much less resonant. The whole idea may require a somewhat elaborate setup to hold the guitar very stable, but I think it could be a fascinating video.

0:07: 🤔 The video discusses the phenomenon of a ball being thrown into a cylinder and coming back out again, exploring the concept of centrifugal force and gravity. 2:23: 🎥 The video discusses the ratio of turns between a ball and a cylinder and relates it to the turntable paradox. 4:55: 🔍 The video discusses the ratio between the wall thickness and the square root of a squash ball, as well as the ratio for a mouse ball, and suggests possible explanations for the differences. 7:32: 🎥 The video explains the intuitive explanation of the gyroscopic effect on a ball thrown in a cylinder. 9:56: 📚 The video discusses data brokers and how Incognido helps individuals protect their data. Recap by Tammy AI

Regarding your motion amplification camera: If you're still looking for ideas, I'd recommend small aircraft. I work at a flight school and it's always amazed me how the vibrations of the engine can ripple through the airframe and have an effect on parts which (to the human eye, at least) seem incredibly stable. It could useful to see the amplified difference between a "perfectly balanced" prop and one which is very nearly balanced.

One mirror over the top of the cylinder would give you two synchronized views.

For the motion amplification, I would be interested to see how houses and surrounding area reacts when a train passes by. Like what effect is the train have as it is rolling across the tracks. We just moved into a house with a set of train tracks behind us and when the train passes by it feels like the whole house shakes sometimes.

It would probably be easier to visualise what’s happening if you'd drawn three differently-coloured circles oriented peripendicularly to each other (like representing x, y, and z coordinate planes) on the ball. It would ease tracking rotation and direction in slow motion.

The closest thing I can come up with to an intuitive analogy for what may be going on is from playing with marble mazes as a child. If you throw a ball bearing around a funnel in an elliptical orbit, you get the same pattern. The ball keeps missing the hole in the funnel and running back up the other side. This shape makes intuitive sense. Now all we have to do to make what the ball accomplishes in the cylinder intuitive, is to slowly augment the shape of the funnel until the funnel *is* a cylinder. Even with the cylinder, the ball is attempting, and is, following an elliptical orbit and "missing" the hole at the bottom of the funnel and running back up the other side. The fact that this works with the completely vertical sides of a cylinder rather than the more angular sides of a funnel, and the fact that it's more difficult to intuit and elliptical orbit inside a cylinder, is where the bizarre intuition break happens.

It would cool to draw dots on the squash ball (or the smaller ball) to be able to track more precisely the axis of rotation (kind of like you get on some pool balls to illustrate the effect of spin).

I guess the easiest way to figure out what happens should be painting the ball on equator and on poles, shouldn't it?

Very impressive analysis . It's great that you take the time and effort to understand something that very few would give a second thought and then make what you discover available to us . Congratulations !

My first instinct was that the ball is essentially bouncing with extra steps. The centripetal force gives enough friction againt the wall that it is able to elasticly return the downward component of your initial throw. The gyroscope effect keeps the ball from just rolling down the wall by limiting its ability to spin in that direction.

The motion amplification camera is the coolest thing i've heard of in such a long time.

I'd like to see the motion amplification of an interior of a car, with the engine running. It would be especially interesting if there were some sort of buzzes or rattles in the dashboard. Hopefully the motion amplification could pinpoint where the noises were coming from, as it can be hard to locate with your ears.

Suggestion for the motion amplification camera: The top of an acoustic steel string guitar. You should see the different modes of the guitar, changing by string and by note. The modes are very complex and would be really interesting to visualize.

If you pay really close attention to the high speed shots, you can visually *see* the axis of rotation changing on the balls by watching their surface texture's spin. You'll notice that the axis seems to "flip" at that midpoint in the osclilation. If you take that initialy intuitive explanation of the ball's axis of rotation remaining the same as it travels around the cylinder, you can very clearly see that happening in every shot (its easier for the hollow ball shots, since its surface texture is less homogenous and easier to discern). But at just about the end of that first go-around you can see the ball very quickly and very suddenly flip its axis of rotation the other way, thuse steering the direction in which it spins. You can basically "trace" their movement along the cylinder and find that it very very closely mirrors that sort of up and down spinny rotation of a spun coin as it nears the end of its spin. The balls in this case are basically tracing the edge of that coin as it spins, first going in a Top-left/bottom-right diagonal and then a Top-right/bottom-left diagonal

For motion amplification you could show cars at a subwoofer competition. It’d be fun to see how the people inside look with it

Put 3 stripes around the ball, 2 from top to bottom offset by 90 deg and a third around the “equator”. Each stripe has a different color. This will help show full motion range of the ball. You could also keep the strips solid color and instead color each of the 8 sections a different color. Then enlist the help of the slo mo guys to do a collaborative video about it.

The intuitive explanation seems easy to come by and you nailed it I think. Conservation of angular momentum where imparted momentum eventually matches velocity at the contact point then through friction becomes an acceleration force through conservation of angular momentum while simultaneously and continuously sustaining additional conversion of velocity to angular momentum to match surface contact velocities at the tangential contact point.

6:58 Wow! I didn't know that this RDI technology was a thing and it's fascinating. I'm so excited to watch your video on this topic that you mentioned. I love learning about something I've never considered before

You could film the top and side view at the same time by filming from the top and putting an angled mirror in frame next to the tube to give you the side view. Kinda like the opposite of how they use a mirror to align two big cameras when they film 3D movies.

For the Motion Amplification Cam, maybe a collab with Look Mum No Computer with the organ he repurposed at his place. There are some huge pipes that will oscilate when the air passes through them and you can fit dozens of these pipes in frame to see how the size affects the oscillations.

For the motion amplification camera, I think it'd be interesting to see motion in various sports contexts. How does a bat, hockey stick, or racket vibrate through impact? How does impact affect the ball? How about the human body? How do our muscles vibrate when running, jumping, swinging, etc.? Hopefully the macro motion doesn't cause any issue capturing the micro motion in these cases.

The behavior reminds me of a ball rolling into and out of a bowl. If it retains enough momentum, it'll pop back out; if not, it stays in the bowl, just rolling back and forth like a pendulum. I think you already gave us an intuitive explanation - the forward momentum leads the ball into the cylinder, the gyroscopic effect wants to roll the ball back out, the frictional force direction keeps changing in relation to the gyroscopic direction, and the three start negotiating with one another. Given enough momentum and a friendly angle, the resulting path begins oscillating between downward and upward. Great video!

Steve is the only person that can actually make me want to learn something I don’t need

I think a cool object for motion amplification video would be a string instrument like a violin or a cello (Maybe a double bass depending on the maximum frequency of the camera) would be cool - there's a lot of engineering of the shapes of these instruments to control the harmonics of the sound. Also, you don't need 2 high speed cameras if you have a good mirror, that way you don't need to sync your camera streams Edit: Typo

one of the best channel on this platform, ever. Thank you again!

@SteveMould, did you try applying the equations of orbital mechanics to it? Orbits are mathematically just sections of a cylinder. The motion of the ball looks a lot like a precessing orbital plane. The ball shooting out occurs when the trajectory matches e>1, which is what we use to slingshot spacecraft around planets.

Usually papers don't have very intuitive math due to how many layers the information is on top of. What I think might be helpful is use the force diagram and simulate how it changes with each time frame. That might be a good place to start

I think it would be helpful to track where the ball is in contact with the cylinder, and then draw/animate that path along the surface of the ball. It's not just rolling along a circular path along the circumference, and I think understanding that is important for an intuitive understanding. Also if you put markings on the ball so we can clearly see how it is actually oriented, that would help to understand/visualize what's goin on.

Medhi recently made a video with aluminum foil balls, where he could have used the RDI technology, to see the small movements of the balls. You two should make a follow up video together about the phenomenon! I would love to watch it happen!

Yes I want to see more with the motion amplification camera! I can think of so many industries and application where that could be extremely useful!

I love following Steve on his journey from bewildering phenomenon to intuitive understanding.

Would love to see motion amplification of a 3D printer, to be able to see the different vibrations that occur as it moves around. A comparison between a cheap and expensive printer would be cool too!

Top notch work and easy to understand presentations.

Musical instruments for the vibrato camera would be extremely cool, especially woodwind instruments where it's kindof unclear where the sound actually happens; for strings its the strings, for brass its the bells, for woodwinds it's generally the tone holes but it would be nice to see that visualized.

Minute amplification ideas: Bathrooms - curious to see how well built a bathroom is - turn on the water and see if there are any movements in the shower/bath. Cars, the car itself and the engine compartment - how does a car vibrate? Nailing up a picture on the wall - sometimes when you nail up a picture, you might popout an old drywall nail; would be interesting to see what vibrations are caused when nailing on a wall. Similarly, jumping on a 2nd story house - the other day my daughter started jumping with joy and I could feel the house framing move as we were on the 2nd floor.

The idea for motion amplification is "How a transformer emit a high-pitched sound?" (if it can register such high frequencies). It might be quite interesting because AFAIK it's because a transformer physically changes its shape due to the magnetostriction effect on the transformer's core.

I can explain this rather easily, I think. The key to understanding what is happening between the ball and cylinder is in analyzing the relative motion of the core of the ball vs. the outside of the ball vs. the cylinder wall. Like a continuously-variable transmission, the pathway of contact determines the speed at which the ball rotates vs. the speed the center of the ball travels across the inside of the cylinder. From the balls' frame of reference, its pathway through the cylinder is no different than it would be through a cone. As the ball reaches a point in the pathway around the inside of the cylinder where it is spinning on a shorter line of longitude, the actual speed of the ball as it travels across the cylinder is at its lowest. Then as the inertia of the ball continues to push it around the cylinder, the longitude of the contact line on the ball grows larger, allowing more of the inertia stored up on the way down to be released into the cylinder wall, which in turn decreases the speed at which the ball is rotating while increasing the speed at which it is revolving around the center of an elliptic section of the cylinder. This increase in speed results in an increase in centrifugal force, which flings the ball *upward* because the downward direction was where it gathered the momentum.

Steve - huge fan of your videos. The discussion around intuition is great. If you stripe the ball with a few colors, it would be most helpful to see the how the axis of rotation is influenced by the wall and rolling.

Motion Camera Idea: Oscillations of sky scrapers during wind storms. From external to internal support structure.

I've heard that up to 80% of the noise a passenger jet makes while in flight is fuselage/wing vibrations. I imagine this would be a massive task to turn into a video, but I think it could be incredibly cool.

Based on your explanation and the slow motion footage, the best way I think I could explain it is similar to your explanation. As you throw the ball into the cylinder, it'll instantly encounter friction against the wall of the cylinder and begin rolling in the direction you threw it. But then, due to the curvature of the cylinder, it'll "roll" (actually slipping) around to the other side, and with your same naive assumption that the axis of rotation stays the same, the ball's original rolling rotation will now be rolling against the direction of its movement and start rolling back up the cylinder. One experiment that might be an extreme example of this is throwing a bouncy ball under a table. You might have done a video on this before, but if you throw a bouncy ball under a table, it'll hit the floor and begin spinning forward. Then as it bounces up, still spinning forward, it hits the underside of the table and instantly gets thrown back out from under the table in the direction you threw it because the forward spin hitting the table produces a backwards frictional force that causes it to bounce back. At least that's how I understand it and it seems like an extreme version of a cylinder. With the cylinder, you then have to account for the spin of the ball constantly trying to match the direction of the ball's tangential movement along the cylinder walls.

How about a motion amplification of a city skyline or a very tall building district during a wind storm? It would be neat to actually see a building with a tuned mass dampener next to one without!

This reminds me of what happens sometimes in basketball where the equator of basketball gets really low on the rim but then the ball pops out anyway. Once I saw the ball go around the rim about 3 times before falling out instead of going through the hole.

I hadn't actually thought about this, having only played a few rounds of mini-golf in my life, but it makes sense, within a certain range of parameters. Without watching more than 5 seconds of the video, what is obvious is that you are getting rotational force input from two different fixed directions but you can only actually rotate in one direction, so since one of the forces is an exponentally decaying linear input and the other is an accelerating quadratic input, the rotation is unstable and must flip, and since flipping is symmetrical and cylindrical holes are symmetrical, there are necessarily cases where the ball just pops back out. Neat!

I wrote basically an essay here just a second ago but I figured I would explain this more Layman's terms. - Ignore gravity so you can see this change to the extreme - ignore the gripping factor, this is taking into account sliding which ignores the force of friction. - Now what you want to know is why it takes this trajectory, we will look at its angular momentum vector in order to see this clearly and make the trajectory horizontal. Like this ^ | ------------------- The area you see here is the trajectory (x axis) and angular momentum vector (y axis.) This vertical line basically just shows the angle that the ball is rotating (think of it as a pen and the ball is spinning around the pen with the pen being the center of the ball). For this angle to change, there needs to be a force which overrides the force holding it upright. We said gravity = 0 before, now lets say the force of gravity increases based on earth. This means f=m*a , on earth (a) doesnt change. So you can only change mass. Considering this, the more mass the larger the force of gravity. Considering the ball is thrown at an angle, then your visual diagram would have a gravity force that is not in the opposite direction of the angular momentum direction, but at an angle like so Like this ^ | ------------------- \

I wonder if you could develop some little magnetic "kicker" to give a tiny bit of energy at the bottom of its oscillation, to keep it going indefinitely, similar to those kinetic magnetic desk toys. I would absolutely love to have something like that as a desk toy.

id like to see a motion amplification video of a jackhammer, where something is actually intended to break, to see if it can predict where stuff breaks

I would love to see the high speed camera applied to both the ball and club of a golfing tee-off. Great video as always Steve!

Per your request, here is an attempt at a simple intuitive explanation of why the ball's vertical travel oscillates at a ratio lower than once for every circuit of the cylinder, the value obtained if the axis of rotation remains fixed. (IDK whether a better explanation has already been posted.): The ball initially enters the cylinder rolling at a downward angle. It has a downward velocity and its initial axis of rotation is at an angle to the vertical. Assume for the moment its axis of rotation stays fixed, and there is no slipping. A quarter of the way around the cylinder the ball's trajectory will be horizontal. Its downward velocity will have changed to zero. One can think of the downward velocity change as resulting from a force applied perpendicular to the ball's trajectory and acting on a tangent to the ball's surface at the point where it contacts the cylinder. That force bends the ball's trajectory. But being tangent to the surface, it also affects the ball's axis of rotation. (The direction of axis change is per the gyroscope effect.) Because some of the force is spent changing the axis of rotation, less remains to bend the trajectory. So the trajectory changes more slowly than it would otherwise. When the trajectory changes more slowly, the oscillation ratio is lowered. Hence the oscillation ratio is lower than the 1:1 obtained if the axis of rotation did not change.

Put a mirror over the cylinder? This way the camera sees both

I've never heard of a motion amplification camera but now I need one! I'd love to see musical instruments, such as guitar strings, drum heads, or even brass instruments!

its easy to think a constant force means constant rate of precession, but not so, it has to accelerate, in steady state yes a constant force means constant precession to maintain conservation of angular momentum, but when it is changing its a bit different, that is where the delay in the non slip case comes from i think. when you arrive at the bottom you have the maximum rate of precession steering upward but 0 rate of change in the rate of precession plus the change in rate of precession from gravity it the rate of change of precession from gravity is always just depending on the angle between the vertical and the direction of motion inside the cylinder, its maximal when the ball rolls fast and the angle is flat and parallel with the circular direction, but at some speed and downward trajectory the delayed rate of precession when you reach parallel trajectory tangent with the circular horizontal direction it is smaller than the upward steering change in precession causing a decrease in the steephood of the trajectory eventually leading to the ball going up again. roughly speaking. i think the intuitive hurdle is basically too get this idea of a torque on a gyro leading to a specific rate of precession out of your head and relearn what happens to a gyro when a torque is applied. you can solve it exactly for the case with no gravity and then think of the height as a change between different solutions to the no external force problem. so as you go down in the potential its a continous transformation into instantanious parts of different non external force solutions. not very intuetive perhaps but its real and true. then the moment of inerta and the hight determines the speed at soem height, and the speed gives you a trajectory for an orbit without any force correpsonding to a small change, like gravity only acted for a breif moment and changed one no external force solution into another non external force solution with the same angles and speed at that point to as you go down it corresponds to the same angle solutions with more velocity and angular momentum correpsonding to different derrivatives, and so you can derrive a change in the changes and get ready to do some crazy maths lol :P. sorry for typos or mistakes.

Further intuitive explanation: The ball is spinning with an angle of rotation perpendicular to the radius of the cilinder. But in every degree of rotation, this angle tilts just a little because the gravity is pulling the ball to the ground while the ball is in contact with the wall so it creates a small rotation in the perpendicular axis. This small rotation that change the direction of the ball is in function of the inercia of the ball: The higher the inercia, the higher the number of turns of the cilinder for every up and down.

Hard drives vibrating can be a problem in server settings (hence the need for server grade hard drives). Could be interesting to see how much they actually vibrate :)

We had a similar problem in our lab where we needed 2 slow motion cameras (we didn't) so we used a tilted mirror. It worked. Nice video

Hi, great viedeo as always! For your camera: Some times, when I stand at a traffic light on my bicycle or even sitting in a car, and a truck drives by on the other lane, I think I can feel a faint shaking of the ground. (But I don't know if this is just the air pushed sideways by the truck instead.) Would it be possible to film a road with this move-amplifing camera and see the ground shacke because of the traffic?

You could allude to the carnival game where people are required to throw balls into a wide pail thats placed at a 45 - 60 degree angle, where the goal was to make the ball stay inside the pail. The trick was to throw the ball with some combination of a bit of spin or at an angle or an arc in such a way that the balls rotation and momentum is cancelled or negated after the first contact of the pail's sides.

Happens with basketball hoops as well, though I’m guessing spin and physical grip has more to do with it in that case.

3:34 Have you considered spraying a hollow ball with something like Testors Dulcoate? Magicians sometimes use it on playing cards to increase friction between two cards. Great video, as always.

If you want an intuitive way of explaining this, I'd suggest starting with pool ball 'english'. In pool, english means we strike the cueball off-center, imparting a lateral spin that interacts with the typical vertical spin of the ball rolling across the table; this makes the cueball swerve in the direction of the spin. So (e.g.) if you were to take out the flat inclined plane you used early in the video, but give the ball a sharp upward twist before releasing it, I think you'd see the ball do a dip and rise before gravity overcame that initial english. What I suspect happens inside the cylinder is that centrifugal force is putting a constant 'english' on the ball, producing a countervailing spin moment by moment. That english occurs because the the ball is in contact with the wall at a spot that is not generally on the rotational equator of the ball, adding a new spin. The ball goes up and down cyclically because the additive directional vector of the spins changes according to the (periodic) precession of the ball itself and the (periodic) changes in the ball's contact point with the cylinder wall.

This reminds me of my intuitive explanation of the gyroscope. I was flatting with a PhD physics student who called my explanation nonsense. He said it was just conservation of angular momentum. It is, but that isn't very intuitive. (BTW, I do have a BSc in mathematics which contained 50% applied maths and physics in first year.) My argument is similar to what you explained in the video. If a spinning top starts to tip it will start to gain angular momentum about a line perpendicular to the axis of rotation. After 1/8 of a rotation that component will be perpendicular to the original direction (explaining precession) and after another 1/8 of a rotation it will be upwards and restore the balance. As there are always such disturbances (wind, vibration) this happens continuously but unnoticeably. But as the top slows down the 1/8 of a rotation takes long enough for us to see the effect and the nutations become very visible. Maybe that would make a nice video if it hasn't already been done.

Could you possibly use your motion amplification camera on a roadway bridge? Not sure what the lenses & technology allow, but it'd be cool to see a suspension bridge, or even just a standard concrete overpass flex as cars go over.

I'd love to see the motion camera filming various types of bridges such as suspension bridges and cantilever bridges. There are three different bridge types where I live and I've noticed, during rush hour commute, that when I put my foot down (on my motorcycle) that the cantilever bridge I cross bounces imperceptibly.

you can think of a gyro with a constant precession rate as generating a force in the opposing direction, so apply a constant torque to a gyro and its rate of precession will accelerate until the rotation rate of the angular momentum axis will produce a torque that opposes perfectly the onoe applied, if that makes sense, parsed poorly, but thats the idea, so a rotating rotation vector corresponds to a torque with a rotation direction, so its kind of what corresponds to two different parpendicular axsheeesh of rotation combined together, which is the kind of path the your fingertips trace out when doing the 720 rotation trick. so in the rotating frame of the gyros angular momentum there will be a touqe 90 degrees of both of the rotation axis that have angular frequency, so this torque can be balanced with your finger for example in free space but then you ofc accelerate the whole setup as well so in a steady state you are doing work on the linear velocity. in the real world you are accelerating and not in a steady state, thats why the intuition of constant rate constant force decives you.

Hey Steve... Even though I don't play squash myself, I understand there are different grades of balls for 'Speed' and those graded balls react differently during the game of squash, as in, as they warm up with the constant hitting of rackets and the wall, they change their perameters of bounce etc... So.. Would different temperatures of the squash ball make a difference in 'Slippage'/grip when performing these tests within the perspex tube and thus adjust the ratio of rotation vs raising & lowering in height? ie a warm/hot squash ball vs cold??? 🤔😏 😎🇬🇧

in terms of the motion amplification camera, i'd love to see ordinary everyday things that people might have at home using it, things like laptops, fans, printer, computer/tv speakers, faucet/tap, kitchen/bathroom pipes, washing machine, microwave, refrigerator, etc. Would be nice to know how much these types of things move over time, what parts may need replacing or something you think should move doesn't move at all

If you ever need 2 high speed cameras you can always use a mirror ;) saves me loads of money.

I think it might be easier to explain as the ratio isn't 1:1 because the wall of the cylinder applies a torque on the ball. That torque has a different effect on the ratio based on the moment of inertia of the ball.

I believe you can simplify this issue with a rubber ball bouncing in a rectangular tunnel. You bounce it off of the floor such that it hits a wall, then bounces off of the ceiling. The first two impacts will convert some of the momentum into spin. When it hits the ceiling, the spin induced by the impact with the floor will exceed the remaining forward momentum, driving the ball back to you. For extra credit, can you tell me why the ball won't hit the other wall?

For the camera motion amplification, id suggest filming the processes of cnc or manual machinery. Theres alot of complications when it comes to cutting metal.

Motion amplification idea: Saxophone. I play bari sax, and I can feel the instrument vibrating differently as I change the notes, especially in the lower register. I assume there are nodes along the brass. I would love to see that!

I think I have an intuitive way of understanding this. As you already mentioned, mathematicaly, this could go on forever if not for loss of energy through air friction, etc. Lets imagine we would try to introduce energy by moving the cylinder in a circular motion, just like we all did as kids :) As you might now from experience, if we move the cylinder really hard/fast, the ball will go very fast in(to) a path of the smallest possible circumference (perfect circle, instead of an oval) within the tube and move on this line until we stop moving the cylinder. As you said, gravity does not have an impact as we can turn the cylinder in any direction without the ball changing its path, given we manage to keep the perfekt rotational movement of the cylinder. This means that the ball is always being "pulled" on this line/path of least resistance. The harder we move the cylinder the harder the ball is pulled onto this line. So when you throw the ball into the cylinder, the ball immediatley starts being pulled towards this line by its centripital force. Looking at the thumbnail of this video, the ball at the lowest point at the path represents the moment when the ball is in fact on this line. However, as it still carries momentum from the acceleration towords this line it overshoots it with a certain excess of force now opposite to the initial direction. Therefore the ball moves beyond the line and doing so the centripital force now works against the current direction, which results in a gradual change of direction. At the midpoint/crossing of the overallpath the ball now has a new optimal line within the cylinder, opposite to the below one with the same distance to the crossing in the middle, as the movement direction of the ball is inverted. Now the same happens again just mirrored. After this the cycle repeats. If we would be able to move the cylinder in this circular way and therby apply just the perfect amount of energy, we could keep this going on forever. If we rotate to hard, the ball starts moving in a perfect circle. Too little and it drops. Even though I did not include any other phenomena which happen at the same time like the rotation around its axis, I hope this makes somewhat sense😅

me at 1:50 - The analysis is of the cylinder. But its about the sphere interacting with the cylinder. Mapping the path in gravity along a flat (angled) surface is not giving the same contact points that a sphere inside a cylinder would give. (continues video) Though it seems to work horizontally.. It seems to exit earlier with the same thrown in angle.. so Gravity makes it stay in the cylinder longer.. Also thinking about it.. there could be a bit of mathematics between the Circumference of the ball and Tube... and the square root of 2/7 and 5/7 ... Also divide by 7 is interesting as 22/7 is close to pi.. (used to use 22/7 to give ball park measurements for things when doing quick circle maths...) The errors from pi could be losing contact with the inside and slipping / skipping the surface. Pretty sure this could be done in a computer model...

Awesome video! I love how you depicted the mental progression towards a hand wavey model (and I totally buy the hand wavey model you came up with!) gotta send this to my mom who golfs a lot…

It'd be interesting to see this experiment done in space.

Your intuitive explanation was the first thing I thought of, and I also noticed that the answer is incomplete because we don't take into account the slight shift in the axis of rotation due to friction and inertia resisting the pull. However, when the tube was on its side, it did behave very similar to what I intuitively thought was happening for both hollow and solid balls. What if in a gravity-free environment the ratio is exactly 1, and it's gravity pulling it down, leveraging on the ball at the point it touches the wall (like a lever where the pivot is the point where it touches the wall and the force is applied somewhere at the centre of gravity)? Maybe on its side, the tube has less of an effect on the ball due to gravity because the wall is only perpendicular to the ground (in direction of gravity) at 2 points on the circle, and everything else is a slope.

By 1:54 i had a theory: the initial 1/3 circle trip around the cylinder imparts a rotation on the ball, and the axis of rotation is something that doesn't tend to change. What's different about the flat version is that as the ball travels in the cylinder, its rotation relative to the point of contact is changing, which means the initial falling spin will kick the ball upwards when it reaches the opposite side of the wall

it will be cool to observe the oscillations of grandstands at a football (UK term) match. Having a visual of the dynamic loading will be interesting to see

I feel like with a specifically marked ball and a fast enough camera you'd be able to plot the exact movement of the ball itself and extrapolate from that. Get Gav and Dan in here

Couple things I want to mention --- i don't think the golf phenomenon is related to this. Golf balls are not high friction and golf holes are not long tubes, they are just short buckets. Golf balls go in too fast and bounce out due to contact with the bottom of the hole. For the intuition on this. So if the ball is frictionless it would travel down the tube in a helix. When there is high friction, the linear momentum of the ball constrained within the tube wants it to travel down in the helix, but as you describe at 7:30 in the limit of infinite moment of inertia and infinite friction, the ball would trace out an elliptical path. Consider the state of affairs leading into one quarter turn. At this region the angular momentum of the ball wants it to ride back up the tube already (elliptical trajectory). But the linear momentum of the ball is going down (helix movement). Thus we have a torque that friction against the inside of the tube would apply, a torque generated by friction pulling up. Basically like when the path is not aligned with the curvature of the tube, then running along the tube with friction is going to apply some torque that is perpendicular to the axis of the tube. In the example scene at 1/4 turn, this torque has an axis (right-hand) pointing in the same direction as the camera is pointing. Since the ball is spinning with the (right-hand) axis pointing down and toward the right, a.k.a the torque and the angular momentum axes are not aligned, this must generate torque induced gyroscopic precession... At this point my intuition breaks down somewhat as I'll need to get my hands on a gyroscope to think through if the direction of the precession makes sense at all... what little feel I have for gyroscopic precession tells me this makes it turn the ball's axis of rotation downward, which seems reasonable, because that is why the ball doesn't shoot back up immediately: it takes a little longer than one turn before popping back out. It's some kind of natural process that when your ball has some friction, the geometry of the tube applies gyroscopic forces that work out always to nudge the ball's angular momentum via precession to turn toward rolling in the same axis as the tube. It does feel pretty natural. There's no reason for it not to overshoot so it just oscillates. It would be nice if astronauts could bring mouse balls to the ISS to test this out. I think it is intuitive that there is this gyroscopic precession at play that nudges the axis of rotation of the ball in some way and it makes sense that the moment of inertia would determine the relative velocity of this precession, but you already covered how that in itself is intuitive.

Hey! A billard-cue hitting the cueball looks awesome in slowmo. Also a pickup on an vinyl LP is pretty cool!

I would love to see motion amplification of various musical instruments! It would be great to see how the body of a guitar moves as it amplifies the sound from a plucked string, or the bell of a trumpet.

I would love to see the motion amplification pointed at some electronics or a PC's internals. Something we think of as being completely still when in operation. Would be amazing to see if there was some vibrations.

I'm not sure if this is a valid comparison, but the first thing that came to my mind was a car on a banked curve: if the car goes around the banked curved too quickly it moves outward (away from the center of the circle) and if too slowly it moves inward (towards the center of the circle). Since the ball is constricted by the cylinder's walls, the only way to go "away" is to go up the cylinder's wall and "towards" would be down the cylinder's wall. When the ball is first thrown into the cylinder, it's moving too quickly and even though it's thrown downward, it'll start to rise up due to the extra speed. As it does this, it will slow down causing it to move back down. I think this makes the bank angle of the track equivalent to the angle you throw the ball into cylinder (not sure though). This theory does not explain the sqrt(7/2) phenomenon (though it might if analyzed more mathematically incorporating the moment of inertia). There is a critical speed for the car on the banked hill problem that doesn't require any friction to complete the turn. If this theory is right, there should be an analogous situation for the ball in the cylinder: turn the cylinder horizontally and if you throw the ball at just the right speed for a given angle, it should show minimal to zero deviation horizontally and more or less stay inside the cylinder. I think.

It seems to me that this phenomena could bring a new generation of particle accelerators. There should be a way to rectify the "downward part" of the oscillation and have the ball going only in 1 direction. Ex: the ball magnet could be spun 180° by switching the polarity of the cylinders wall with electro magnets at the right time. Or Have a cylinder with split magnetic polarity on its lenght, and throw a bismuth ball into it, or an aluminium/copper/gold maybe lol. I dont know. Very interresting videi! Thanks for sharing. I didnt know bout that at all!

Hi Steve ! IDEA I would love to see : motion amplification of the modes of vibration of a guitar top, a little bit like Chladni patterns. And then try other kinds of instruments to see how they behave differently.

On the matter of viewing the setup from two different angles simultaneously, you could probably pull this off using mirrors to reflect the two perspectives into the field-of-view of a single high speed camera. I haven't taken the time to figure out the specifics (something like the mirror arrangement used by Newtonian telescopes perhaps? Maybe incorporating a second arrangement of mirrors like a periscope to first shift the light's path to the side so that you needn't reflect through the cylinder itself?), but it ought to be possible.

For the camera, have you thought of applying it to acoustics? I’ve seen some high school math projects about wavelength acoustics in pvc pipes at different sizes and widths. Would you be able to use the camera to show the differences in how the pipes vibrate at different notes and octaves?

You could record the top view and the side view with one camera if you place a mirror at an angle above the tube opening. That way the camera would see the side view directly and the reflection of the top view through the mirror within the same frame. No need for two cameras or to sync up two video files in post. (Referencing min 2:51where you wish you had two cameras to film.)

That motion amplification camera is so cool, never thought of one being a thing, but sounds super useful! I would be curious to see the affects of sound waves (Or different frequencies) has on objects. Maybe to demonstate a resonant frequency?

So I can blame science for my terrible golf scores and not the fact I am terrible at golf 👍

For the motion amplification, a really good use would be cardiac physiology. Highlight things like the subtle motion of the cardiac apex under the chest wall or even better, the dreaded waves of the carotid pulse.

Thank you for labelling the mold, I would never have guessed you were cast out of something that shape.