The Spool Paradox

The first 100 people to use code SCIENCE at the link below will get 60% off of Incogni: incogni.com/science
Spools can behave in counter intuitive ways. The puzzle get's even weirder in the limit as the spool gets full, and then goes beyond full!
Check out the Physics Girl video here: • SPOOL RIDDLE - Which w...
You can buy my books here:
stevemould.com/books
You can support me on Patreon and get access to the exclusive Discord:
/ stevemould
just like these amazing people:
Tj Steyn
Pavel Dubov
Lizzy and Jack
Jeremy Cole
Brendan Williams
Alan Wilderland
Frank Hereford
Lukas Biewald
Damien Szerszinski
Heather Liu
Grant Hay
John Zelinka
Paul Warelis
Matthew Cocke
Nathan Blubaugh
Twitter: / moulds
Instagram: / stevemouldscience
Facebook: / stevemouldscience
Buy nerdy maths things: mathsgear.co.uk

[@SteveMould]

I know some people get salty when I use the word paradox. And I get it. Like, if it's not a logical paradox, I'm not interested! But I think "when I pull on the rope it gets shorter" fits the Merriam Webster definition quite nicely. And, you know, it makes for a better title. The sponsor is Incogni: The first 100 people to use code SCIENCE at this link will get 60% off: incogni.com/science

[@sprucemaroose]

I'm fairly satisfied with a paradox being defined as anything that defies normal logic without an obvious explanation.

[@cdscissor]

I believe jan misali's video on paradoxes where he defines different kinds of paradoxes will be an interesting watch for you.

[@NightKev]

Just point those people to Jan Misali's video "the five kinds of paradox". 👍

[@MarijnRoorda]

I appeared to have learned something from this video. I'm not sure what exactly it is that i learned, but i feel smarter... Would that be a paradox?

[@thepenguin9]

It's a paradox of expectations. All the normal rules tell you it should roll away, but yet it gets closer and betrays the expectation

[@HimanXK]

The way this guy breaks a problem down and finds the answer then explores all of the related problems is always really amazing. Great video as usual.

[@KGBos]

My thoughts exactly!

[@retrorevival1]

Big props to Diana and everything she does with Physics Girl. Spool Paradox aside, wishing her a speedy recovery from long covid (bed bound for almost 6 months now).

[@JokeswithMitochondria]

Diana is awesome

[@retrorevival1]

@@JokeswithMitochondria she's amazing, and bless her husband and everyone around her doing their best to help her right now.

[@tomhappening]

Diana is a poser. She doesn’t know anything at all

[@justins8802]

@@retrorevival1 If there’s a heaven, I’d like to think he’s already punched his ticket.

[@pafnutiytheartist]

She'll be in heaven with Terry Devis soon 🙏

[@heatherjohnson2301]

As a Civil Engineer, this is such an excellent lesson in statics! The pivot point (or moment center or center of rotation) works perfectly as statics says it should! Bravo!!!

[@SuzukiKid400]

As a mechanical engineer, this is a better lesson in kinematics to illustrate mechanical advantage/gearing principles.

[@lordlucan7655]

But can you explain how it is when you drop a roll of toilet paper , it always rolls away until there is no hope ?

[@gwynm8506]

A true physics mystery

[@alyx6427]

depends how you pull it

[@Furendz]

Friction. It takes less energy to roll away than to roll in.

[@francb1634]

I love Steve's mildly alarmed/concerned expression while delivering "the spool has the mechanical advantage over me.. right?"

[@TheGreatAtario]

Reminded me of a classic TV Tropes "String Theory" moment

[@reidprichard]

I think the confusing thing is that we typically think of spools as being fixed at their center. In that case, tugging the cord causes a moment (torque) about the center, causing the spool to unwind. Here though, the spool is fixed to the ground, so tugging the cord causes a moment in the opposite direction (the ground is on the opposite side of the cord compared to the spool's center).

[@MikkelHojbak]

I would have done the analysis with the center of the spool as the reference point. You just have to realize that the moment caused by the rim on the ground will be greater than the moment caused by the string, since the distance from rim to the center is greater. This means that the direction the rim would turn without contact with the ground is the one that determines the actual direction of motion. I like this better, since it doesn't include the moving reference point on the ground. It just feels more natural to me.

[@QDWhite]

Instantaneous Centre of Zero Velocity is a hard concept to wrap your head around. It was for me anyways.

[@pyropulseIXXI]

Tugging the cord does not cause movement in the opposite direction.... it literally is pulled towards you, which is obvious and is moving in the same direction as the pull What would be incredibly weird and confusing is if it moved in the opposite direction to the pull

[@DrDeuteron]

YES.

[@stapuft]

but its NOT "fixed" though, its able to move about freely, if it was fixed, at the pivot point (the center of the wheel) then it wouldn't move at all, but the rope would still unwind.

[@frankmueller25]

Love how he is teaching us how to look at things from a physics-based perspective.

[@keithg460]

7:12 blew my mind. I paused the video beforehand and figured out that it would roll away from you, but I got stuck on the problem of trying to figure out where you could drag it. Wonderful, clear visual used to explain it. Very good video.

[@bungalo50]

I love watching a 10 minute video that feels like 2min since it's so entertaining but also makes me feel like I just spent 3 hours with a physics teacher

[@Tremor244]

3 hours? more like a college semester, lol

[@samuelosei-nketiah2130]

I believe what gives that feeling is the lack of any background noise or music. Nothing that draws even the slightest attention.. Just pure silence. It's a good feeling! I like it too.

[@samuelosei-nketiah2130]

Plus his tone is great to listen to

[@SkyBlue-cv8qb]

You know it's gonna be a good video when steve says "What happens in the limit?" less than 1 minute in

[@Awwwsnapshazzam]

@Repent and believe in Jesus Christ bro what are you on about? When you do this type of thing it does the opposite… you are making people like me despise organized religion… How would you like it if I said don’t believe in anything it’s hopeless save nobody and die… you don’t like it either so shut up

[@Runnerun]

@Repent and believe in Jesus Christ 10:18 10:18 10:18 10:18

[@Deja117]

@Repent and believe in Jesus Christ You are welcome to your religion and I will make no judgement for you believing in it. But please bug off and get a life, whoever is making these bots really must have a sad life to keep them running like this rather than spending that time with loved ones or doing something productive. We all know of religion, it's our choice, go away, thanks. :)

[@alexandermcclure6185]

@@Runnerun wtf does this have to do with christianty???

[@tomuchfunwithgas846]

I love this, you make my 80 yr old brain work. Thank you Steve.

[@rhysdavy5032]

As an electrician this phenomenon isnt new to me but the explanation you have provided is excellent!

[@-danR]

I've never heard of this paradox before, but looking at the 0:30 mark, it seemed a mechanical solution was immediately obvious: forget the cord, think of a stick affixed with a free-hinging bolt to the reel at the bottom point of the spooled-cord's diameter. Pull a few millimeters and which way will the spool roll: It can only be one direction. Go back to the cord: it's a ... 'stick'... of continuously increasing length. If that's the conclusion of the video, I've self-spoiled the plot.

[@DiscoFang]

As an electricain you'll also know how to overcome the paradox. Yank the cord with a sharp pull to overcome the friction and you can get it to spin and roll away from you.

[@TheSkyIsMine20]

I was gonna say something similar you don’t even have to do that just change the way you pull instead of pulling just straight towards you give it a slight incline

[@orangemonkeykiller]

I came to the comments to say the same thing

[@xaf15001]

​@@DiscoFangas a beyblader I second this

[@chrisblake4198]

I'd love to see a follow up to this examining yo-yo physics. I've always felt like there's a lot of interesting things happing when it comes to getting the toy to spin at the end of the string vs getting it to catch and wind.

[@bappyplays]

would LOVE to see a deeper investigation of that

[@undine120]

@@bappyplays I mean, it's just friction versus not-friction. When it's free-spinning, the rope doesn't catch. When you make the jerking motion, it introduces just enough extra tension to get friction to engage again, and the momentum of the spin rolls up the string.

[@bappyplays]

I get the theory, what I don't get is why it's so hard to achieve lol

[@bubbleyboy]

I was thinking the same, but with a diabolo. Possibly easier to construct diabolo with a wider axle, as well..?

[@martijn3463]

A yoyo is a lot less interesting because there is only one force applied to the yo-yo, it's just the momentum that winds it back up, combined with the little pull you give it just at the moment it's completely rolled out.

[@armadillito]

I love how you link this back to simple intuitive llines and ratios of the geometry. And props on making good use of your 3-D printer to improve your demos!

[@chrispycryptic]

This is the most beautiful thing I have seen in quite awhile, exquisitely thought provoking. Thank you good sir for such lovely content.

[@AmphiptereSiX]

It's funny how your first explanation felt more intuitive to me than your "intuitive" one right after lol. Excellent video so far! Edit: the toilet roll example was genius! 😂 Edit 2: I'm always amazed how well you explain complex physics concepts in such a way the most laymanniest of laymen can understand. Thank you Steve!

[@ryanqvincent144]

Me too. :) When I first came across this puzzle I thought of it as a 'friction' issue. If the weight of the spool will prevent sliding than it must roll towards you. I didn't understand all the physics / maths. I really enjoyed the analysis in the video. Made me smile and understand. :)

[@widgget]

same

[@TobiNightcore]

Yea, it should be his middle name "Steve Layman Mould"

[@SupremeDP]

Same.

[@Bibibosh]

Please make a edit 3

[@thooke222]

When I fully loaded my thread spool and created a singularity, it totally destroyed my kitchen. No light has escaped the room since, and I feel drawn to the kitchen more than ever.

[@camyota]

I actually experienced this for the first time just a few days ago. I was unrolling a spool of wire and sort of knew it wouldn't work and I'd need to flip the spool over but I'm hard-headed and figured I could overpower the effect and force the cable to come off of the spool.

[@vexaurora]

I'm always impressed by how well you can make these topics and ideas so grounded and intuitive, thanks!

[@AMorphicTool]

I actually know this intuitively from running cables during an industrial machine install. We often need to run cables 100m+ and they come in big spools. Quickly learned that if we pull the cable off an underwound spool on a lower elevation, like underneath a walkway, we could just pull it on the ground and the spool would spin on the spot, the magic angle 2:45. If the spool ever tried to move towards us, the tension in the cable would bounce it back and keep it spinning in place. If it ever ran off in the other direction it would eventually roll back to it's original start point. Takes a bit of practice to get it right but when you do you can unwind a spool super quick. Kind of fun too. Saved a few minutes setting up some health and safety approved rig to run the spool from. Surprised to see my job reflected in such an elegant manner. Nice work.

[@jimited1]

I never knew I wanted to hear an in-depth explanation on spool rotation and pivot points, but here i am! It is absolutely fascinating! What a great video😲👍

[@easyefpv6609]

As an electrician that deals with spools of wire. I have been obsevering and testing different angles as you did. Love seeing videos of stuff I have myself tested and pondered 😂

[@masterchiefer25]

Love this. Reminds of all those trick questions on physics exams that were always so much harder than anything that was gone over in class

[@kinexkid]

I would have loved to see what happens in the second set up where the rope is just barely above (or rather below) the radius of the inner wheel, and you unwind it to a point where it reaches the same radius length. Does it slowly come to a stop? Does it have enough momentum to flip to the other side and reverse direction?

[@tristanrhines1613]

we need a follow-up on this

[@SuperStrikeagle]

If you have a perfect non-slip condition, it would probably become a harmonic system that "waddles" around the equilibrium point (considering that the system has som damping, reduction of movement) so that in sufficient time it would simply stop. There is a much simpler solution to this problem considering torque: When you pull the rope, there are 2 forces at play, the force you are applying, and a reaction torque from trying to spin the wheel, this torque creates a reaction force at the contact point that is equal to : F*radius of rope/radius of wheel. When you make F - Freact, that defines the way that the spool will move, when F react is greater that the applied force the spool moves away from you.

[@kinexkid]

@SuperStrikeagle That's how I thought it would play out, and it would be really cool to see it in action if there's a follow up video on this. That also got me thinking of how the system would react if instead of a continuous force applied to the rope, you applied a "pulsed" force and what the equation of motion would look like to get it into a stable harmonic motion about the inflection point going back and forth in opposite directions from each pulse

[@TheNathanCater]

This would be a great experiment combining both situations. If the inner diameter was smaller than the outer diameter, and the rope started with a radius larger than the outer diameter I believe you would see a change in direction due to imperfect conditions. The point where r = r is an unstable condition so unlikely to stay there.

[@SteveMould]

Damn, I missed a trick there. Would have been fun to try that!

[@robertmiller3590]

I found this video very interesting! I am currently taking a pre-calculus class in college right now (getting my bachelors in mechanical engineering). but it was very interesting to watch this video and see the things that I've learned about in my calc class, like limits and sine being used in a real world problem such as the spool paradox! it also shows me how closely related math and physics are, which is also super duper interesting.

[@someguy6152]

I remembered as a kid finding this, not sure what was going through my head at the time, but I found the point that it rolls neither forward nor backwards. I remember also finding that if you pull fast enough the spool will either move back slightly or not depending on the angle at all than rush forward because the momentum of the spin still continues after you run out of rope

[@PhilipKloppers]

I've often experienced this practically when installing ethernet cables and pulling them off the spool on the ground - the spool always rolls closer to me. Thanks for explaining it so clearly!

[@GeekOfAllness]

Then you just yank it really hard to overcome friction, then end up with four times more than you needed, then the spool crashes through the excess cable and kinks it when it finally grabs traction and accelerates through everything. Then you invest in a rack with a rod to put the spool on.

[@Scudboy17]

I love the fact that by changing the ratios of the radius of the spool and the cord you have a trade off in mechanical advantage that works pretty much like gear ratios. The greater the radius of the cord is over the radius of the spindle the more you trade length of cord (a large gear) for a faster rotation of the spindle (a smaller hear). I think its fascinating the way the direction of the advantage gets applied changes as the point of exertion moved thru the pivot point.

[@samkass9039]

I was waiting for him to do the case where the rope goes a little under the table, but the spool is above the table, so as the rope is pulled, it first goes one way, then reaches even with the table, and then... would some kind of momentum allow it to get past that zero point and start coming back? Or would it need a tiny push?

[@willkillyaquick]

This kind of reminds me of how pulleys work and torque. Nice shout-out for Physics Girl. Hope she gets well soon. ❤

[@garethkelleher7004]

so what would happen if the outer radius goes from being bigger than the inner radius to being smaller? In other words what would happen if R > r becomes R < r while pulling the string?

[@yannickb1468]

Hey, I started watching your videos not that long ago and I just wanted to say that I really like them :D Especially these 10min ones were there's still a new concept or something to think about and train your physics skills. ^^ Thank you for that and have a nice day!

[@MrARock001]

There's another configuration you could consider: the rolling surface (hub) of the spool is some intermediate value (using the rails setup would work) but the actual inner limit of the rope layer is inside of that. So the rope could then go from having a radius larger than the hub to having a radius smaller than the hub, as you pull more rope. I think this would result in the spool at first rolling away from you as you pull rope directly away from it, to it eventually rolling back towards you as the rope comes off and its wrap radius shrinks to below the radius of the hub. But would it make that transition? Because at the moment of the two radii being equal, there's no pivot at all and friction and momentum would fight for dominance. And interesting experiment indeed!

[@BlazzaBlu]

Exactly what I came here to say!

[@sizors4448]

That setup would result in a stable equilibrium! If the rope is larger than the spool, it would roll away until the radii are equal, and if the rope is smaller than the spool it would roll towards until equal. Any perturbation would tend towards equal radii. It would be cool to see this setup in action!

[@BlazzaBlu]

@@sizors4448 suddenly momentum plays a much bigger part here. If you get the spool moving in either direction then give it slack, it will continue to roll past the midpoint, then when tension is added again it will head towards the middle again. I feel like there's a practical application in here somewhere, maybe to smooth out the velocity of something being pulled along?

[@miff227]

@@BlazzaBlu The Mould Engine

[@miff227]

i mean...I've probably already invented that in my kitchen washing up I haven't done but.....

[@adityashukla7849]

I remember having all this experience while playing with thread spools when I was kid. Thanks for explaining and bringing back the memories.

[@udadni]

I really enjoy how much this channel seems to subscribe to the idea of "Under-promise, over-deliver". The titles/thumbnails are always interesting, and enough so that I decide to watch, but the videos always end up being even more delightful than I expected! It's like the opposite of click-bait?

[@LouisD2023]

Great video. Went to watch Diana's (Physics Girl) video and learned that she has been fighting severe long covid symptoms for several months. So sad. She seems to be a very inspiring person.

[@LivvieLynn]

I checked a few months ago after not seeing videos for a while. It's really heart breaking to see what she's going through. I really hope she improves to the point where she's able to do some activities again.

[@MrDasbinich123]

I personally found the "pivot point" way of explaining it very helpful, thank you for including it, even though you preferred the other version. :)

[@tylerbakeman]

Intuitively, A wheel with a spool being pulled, has a wheel radius W, a spool radius S: If S < W, then the wheel will roll in the direction of the pull, increases the spool radius (with mechanical advantage). If S > W, then the wheel will roll in the direction away from the pull, decreasing the spool radius (with mechanical advantage). It appears as though S -> W when being pulled, no? Friction can decrease mechanical advantage in this model.

[@davidRKjunior]

This is a practical and easy way to understand how the gears on bikes and cars work. For example, why we use less force or more force to accelerate and gain speed, depending on the gear we're using. Amazing!

[@RishabhSharma10225]

Man! This problem always puzzled me in high school and I'm SO HAPPY you made this video, with the intuitive explanations and exploring the different configurations.

[@intothegreatwideopen2]

You're always amazing to watch Steve, you explain technical and unintuitive things in thoughtful way. Hope all is well.

[@Nemz0r]

I was chuffed that my intuition about the thumbnail (I know you change these sometimes so it was of what's happening at 6:28) was correct! There was still a lot to learn from the video though and it solidified my understanding! The way I thought about it was like bicycle gears: When the windings are larger than the tube in the centre and the string is pulled parallel to the axis of travel, it's like a low gear (opposite to actual bicycle gears because there's no wheel as a third part in the system), and like when you're in a low gear on a bike, the force pulling to the right through the string (equivalent of force on the bike pedal) is small and the displacement is large: you pull more string than the travel of the spool (equivalent to rotating the pedals more than the wheel). You increase the ratio of the torque of the spool to the linear force pulling to the right above 1. The string unwinds a lot to the right, but the spool rolls a little to the left. Reverse this, like in a high gear on a bike, and the force pulling to right through the string (equivalent to the force on the bike pedal) is large and the displacement is small: you pull less string than the travel of the spool (equivalent to rotating the pedals less than the wheel) and the spool catches your hand. You decrease the ratio of the torque of the spool to the linear force pulling to the right below 1. The string unwinds a little to the right (or it would if the spool didn't roll that way too!) and the spool rolls a lot to the right. If you change the angle of pulling to vertical, the spool goes left instead as you're no longer opposing and overcoming the spool's torque now, you're just pulling up against gravity and the only sideways force is that coming from the spool's rotation. I enjoyed thinking about this! Keep up the great work!

[@ethanmessinger4798]

I just took statics for engineers and now I'm in mechanics and I found this so fascinating!! Thank you!

[@jajssblue]

I think I played with spools enough as a kid that this paradox is actually intuitive. But doing the calculations is definitely the hard part!

[@connorjensen9699]

A tape dispenser can be really interesting in this vein. pulling the tape obviously unrolls the spool, but you can also roll the spool backwards and you get a really neat result where the tape is both unravelling and wrapping around the spool backwards. Its comparatively simple, but still quite neat

[@spacecowboy2k]

How about the X-rays that scotch tape emits?

[@djknat]

I wish I had a teacher like you when I was taking trigonometry.. and/or chemistry... and/or physics....... hhh and computer science.. You spend time to answer the questions that one would have after a rudimentary tutorial of a basic concept. The way you explained it made sense for the reasoning behind the function. I'd always memorized all the functions but no teacher took the time to explain what the pieces are doing. I really don't even know how to say what I'm trying to say! But, thank you. You just connected dots that I haven't thought about in 10 years.

[@coolbrotherf127]

As someone who used to work with wires in spools like that every day, I was wondering if there was something surprising about what would happen, but nope it reacted exactly like every spool does when you pull the wire from it.

[@OscarHernandez-cb8vj]

My test is tomorrow, and you solved the last question I had inside my head. Excellent explanation.Thank you!

[@GarrieMcLaws]

When Steve made the insert to make the axel even smaller, I thought, I can't wait to see him make an insert that increases the size of the axel so there is a point where the rope is outside the radius of the roller but also there is points where the rope is inside like a regular spool. What happens when the rope transitions through that point as it is wound/unwound.

[@raniz85]

Yeah, I wanted to see that as well

[@Susul-lj2wm]

using a setup like you showed for R < r, you could actually also achieve R = r while still being able to pull the rope. You might be able to get it into an oscillating motion aswell, with a bit of finesse

[@Bunta1987qwerty]

This is actually the type of problem that came up a lot in my dynamics class, with different radii, slopes, and coefficients of friction. Very interesting mechanics.

[@neilpetrarca7395]

I love how every initially wrong intuition has a near case that makes your intuition correct. I thought the spool would run away... And it does at the right angle.

[@UsamaIndieDev]

The only channel that engineers who aren't engineering anymore to always come back to for little enhancements in their knowledge. Love it!

[@TacoMan99]

I work in a hydraulic shop and deal with spools of hose all day. It’s a really funny physic when pulling a hose while the reel rolls back and forth. I never understood it until now. Good video 🔥

[@user-qz6ix7od3b]

the bot that stole your comment has atm 358 likes. those actually belong to you 😄 the problem i guess is that you don't have a profile picture with an ass sticking up like the bot does 😆😆

[@pwagner650]

You rock, Steve! Thanks for making by day brighter and the internet a better place!

[@solarsynapse]

Excellent! Explains the various setups I experience when pulling data cable.

[@jamespeck4895]

This reminds me of the differential chain hoist. Vexing at first sight but makes more sense the more you look at it. You might want to look into it as it may play into the chain fountain if you get it going fast enough

[@ameyabulakh3394]

Yes, and also I remembered about the bicycle. The rear wheel and the chain acts similarly like a spool and rope.

[@mr.cheddar2111]

The last little bit with the tiny spool reminds me of bike gears, a smaller back gear means more pedaling but it’s easier as the smaller radius means you can get a full rotation of the chain around the gear faster but you’ll move less. Great video, I always love how you break things down and try to find an intuitive solution that can make sense even if one doesn’t know all the maths.

[@pauls5745]

I think you mean a smaller front (pedal) gear. lowest gear is the biggest rear sprocket (driven) x smallest front(driver).

[@mr.cheddar2111]

@@pauls5745 ah yes, I haven’t been biking in a while I always mix up which is which.

[@timfieldsend816]

Wrong

[@mr.cheddar2111]

@@timfieldsend816 see my reply to paul s above

[@EngageExplore]

I just love the way you made this video analysis.

[@pepp82]

thanks for putting the read at the end, I always watch those and skip the ones that is in the middle

[@Yezpahr]

6:06 What happens if you put the axle of that spool on a 26.5 degrees slope and have gear teeth in it that slide neatly into sockets on that slope. Could it lift, for example, stones by having it slide down the slope? This sort of contraption somehow feels related to the Grand Gallery of the pyramid(s), which have a gallery with angled slopes with weird slots almost reminiscent to being made for gears with oddly (but accurately) spaced teeth.

[@LunarcomplexMain]

As someone who worked as a broadcast engineer for a very well-known news network for years, you'll run into this type of weird stuff way too many times, thanks for the explanation Steve!

[@leorenegade2103]

Wow.. I think you always going to be my favorite science tuber... Thank you, this was REALLY interesting.

[@terrymoore4238]

Beautiful explanation. This is the same paradox that I heard back in about 1963. Hold a bicycle upright with the pedals vertical. Push backwards on the bottom pedal. The bike moves backwards. This depends on the gearing to make it like the case of your experiment with the rope below the table. I realised that with low enough gearing it would be like your first case and (with sufficient friction) the bike would move forwards.

[@kaboomgaming4255]

I can't believe you didn't let us watch the spool roll up really fast in the last clip with the really small axle. It would have been so satisfying

[@curtisbme]

@0:13 - CORRECTION - Physics Girl was 28 years old in that video, not 6.

[@hhjpegg]

lol

[@cat_with_sunglass]

He means that the video is 6 years old

[@curtisbme]

@@cat_with_sunglass If you read something that is an absurd comment, assume it is a joke.

[@PowerElectronic]

Your content is brilliant. Your delivery is excellent. Thanks

[@skeltek7487]

The Spool problem was a 15 minute test during my first semesters auxiliary training classes for experimental physics at university. Especially the top students wrote several pages of equations and stuff and even them got the wrong results. I spent like 12 minutes of just thinking, before I wrote down the angle for equilibrium and justified it with the tangens of inner and outer radii, with the point touching the ground being the analog to a lever anchor. I finished the ask in 14 minutes, because I was unsure of the slution being that easy and spent half the time verifying whether or not I made any mistakes.

[@theaman5052]

Great video! If your spool starts bigger than your radius and moves away, but as you keep pulling the radius of course shrinks, eventually back smaller than the spool edge, will it change direction and move back towards you? It seems that it would logically work like this but I'm curious as to your take? Thanks Steve

[@PeregrineChurch]

I was thinking this as well! Would be fun to build

[@SillyMooseMedia]

I was hoping to see this variation in the video. I assume you're correct and the spool will gradually slow to a stop as the two radii approach equality, and then roll back towards the direction of the force.

[@markorezic3131]

What would happen in the rope radius > spool radius case if while unrolling the rope radius became less than spool radius? I guess it should then reverse the direction in which you are moving it?

[@ZJasmineDragon]

this is one of those videos where, every single piece of information is something you've experienced in the real world, and therefore know the answer, but its just so cool seeing the break down of forces

[@enjoibrian]

Great video. I would have loved to see a setup at the end where the acrylic portion was used as the pivot point and rolls away from you until the rope radius falls below the acrylic.

[@aanchaallllllll]

0:00: 🧵 Pulling a thread wrapped around a spool causes the spool to roll towards you and the cord to get shorter. 2:01: 🧵 The video discusses the relationship between the distance the spool travels and the amount of rope unspooled, and how pulling the rope affects the spool's movement. 4:00: 🔧 The video explains how to calculate mechanical advantage and discusses the advantages and disadvantages of using a spool. 6:30: 🔄 The direction the spool rolls depends on the force applied to the rope. 8:35: 🔒 Incogni automates the process of contacting data brokers to stop and delete our data, providing a dashboard to track progress. Recap by Tammy AI

[@ch48_]

What if we had a spool that had a radius that falls between its maximum and minimum "rope capacity"? I'm talking something similar to the spool at 6:05, but with a slightly larger radius of the outer cylinders. My first thought is that it would work kinda like a horizontal yo-yo that changes direction as the rope's radius crosses the outer cylinders' radius, gradually working its way towards some kind of equilibrium. Am I on the right path here?

[@DirkLarien]

Love it. It This great start to explore mechanical transmissions and various geared mechanisms. Quite the mind twisters.

[@RufusVIP]

I really enjoyed this, very well put into words a phenomenon that I’ve witnessed but not understood why.

[@frogz]

dont forget to follow physics girls, diana is sick and recovering right now and is a awesome person!!

[@maxtherealone5491]

I wonder, if you made the ruler table long enough, if the spool would flip direction (because enough rope would be lost to pass back over the ruler). At the point when it flips would it have infinite mechanical advantage?

[@connorjensen9699]

I think you would also need to widen the roller part of the spool for this slightly, otherwise you would run out of rope

[@dragonrider9051]

Was wrapping up an extension cord on a spool when I came across this paradox, very well explained thank you

[@maxgotts5895]

This was SO good. Perfectly paced

[@sprucemaroose]

Horizontal yoyo? Hoyo?

[@TLguitar]

3:12 UGH! What happened to your hand?!

[@RC-ij4je]

This was on my Dynamics final exam. Glad the KZbin knowledge paid off!

[@bandola4708]

You're so freaking good at what you do! Another amazing video!

[@AlbionSupreme]

This man is smarter than me

[@bubbafats6246]

too bad toilet paper rolls dont come back

[@Me-0063]

For some reason this masterpiece of a comment is at the top of the comment section for me. Top notch humor 😂😂

[@billj5645]

As an engineer I immediately recognize that this is a form of structural analysis we call "statics". Statics relates forces, angles and distances and as you showed when the force acts at one location with respect to the pivot point, the instantaneous pivot point, it shows how the object will react. You don't even have to consider spooling/unspooling and length of rope although those concepts can't be violated either.

[@Bpyer1]

6:04 The one thing that lacks here is an example with this 2nd set up and the same case as before - when r < R. Theoretically it should also move towards you, but will it? I am not sure.

[@RareEpicness]

man everytime I see physics girl im just reminded of her situation right now. hope she can recover asap

[@blaximum]

Feels illegal to be this early!

[@Agus-fw7dl]

Ikr

[@gehteuchnichtsan7911]

Ich produziere eigentlich eher hip hop aber auch hauptsächlich groove orientiert und ich würde sagen bei groove geht es um spannungzwischen den rhythmischen elementen. Deshalb funktionieren so mini breaks immer extrem gut weil man die drums erwartet sie aber aussetzen und eine apannung erzeugen. Wenn sie dann wieder einsetzen ist es super satisfying

[@Dominasty]

I can't believe...I found something so simple, so fascinating. Nice video.

[@awesomeguyvigil]

first thing I thought of was a yo-yo tbh.

[@Ebay772488]

You discovered Yo-Yo's congratulations

[@HypaBumfuzzle]

Hello Ian, I like your humor, I'm glad you're in the world. 🤣🤣🤣

[@SaquibFaisal]

Unfortunately that's not how yo-yos work

[@bobnoble6476]

this video has melted my mind several times.

[@ATAsgard1]

You are fantastic! I wish people like you taught more things.

[@roberthaines4221]

Mind: BLOWN. Thank you, Steve!

[@XaadeTheBlade]

3rd way of thinking about it. Pull on chord, object wants to slide towards you. Friction on wheel makes the wheel turn, same as if you pushed it from behind. Since the chord is above the edge of the wheel, the differential causes the wheel to spin faster than you expect.

[@hoguesteele]

I'm only 3 minutes in but this is already one of my favorite Steve mould videos. Fantastic

[@alexanderekman7864]

Great video! It would be great if you checked what happens in the transition between the two cases, as the unspooling rope passes the radius in contact with the rails. This could be done by having the rope spooled on a tiny radius core, with a larger radius riding the rails.