The best or worst fact you'll learn today is that no matter how good you are at an olympiad, remember someone had to design those problems first.

Instructions unclear, pencil rolled on the air

I am just shocked how less of physics and chemistry channels are on KZfaq as compared to maths keep going!!! Uniqueness is the key to success

The quality is amazing for such a small creator, love it

holy handwave, batman. that 58% is the most important part of this calculation but it's "left as an exercise to the reader" haha

For the ones who are curious about the loss of kinetic energy: it happens when the axis of rotation (the edge in contact with the ground) changes. Basically at the instant the axis change there is conservation of angular moment (i.e. the force from the ground plane has no torque about the axis) . So, you can calculate angular moment right before impact with the equation that relates the angular moment of the axis about the center of mass with an arbitrary one and the angular moment right after impact simply by angular moment about the new axis of rotation. Due to the conservation of angular moment you know both of those must have the same result, but the first one is a function of angular velocity before impact and the second one a function of angular velocity after impact. Those velocities are different and by equating the angular moments you can find a constant that relates them. Say we call that constant b. Now we see how this affect kinetic energy: at any given moment it is proportional to the square of the angular velocity of the moment. So from a moment right before impact to a moment right after it is multiplied by our constant b but squared. That b squared must be 0.42 and represents how much of the energy is conserved. 1 - 0.42 = 0.58, that is the 58% that is lost. To verify it all we would need is the moment of inertia of the pencil about its center of mass and about the edges Hope my explanation was understandable, I'm not very good at English :p

Damn, KZfaq JUST had it in mind to recommend this channel to me, and your animations and awesome explanations got me hooked. Sad there are only 5 videos, but I can tell it requires a lot of work, and you may not be getting the traction you need and deserve. Gonna do my part and spread these "limited-edition" videos to more of my nerdy friends for sure. These are seriously amazing!

After looking at the vid and before looking at the comments, I thought that you had at least 100k subscribers. You will grow a lot in the future, your content is so good

how did we get the 58% energy loss estimate? wonderful video! Unfortunately, the link to question/solution is not working :(.

Didn’t find a single other video outside your channel solving an IPHO question. Thanks

Thank you, good video! Did you ever make the video to explain how to get the 58% figure at 8:20?

Great video.. dude. You have no idea how awesome a job you have done. How does pencil lose 58% of KE... Can you explain that part?

well, i found 3b1b's brother

Proffesional video analysis!!! Its a wonder that you have not yet reached 100 k subs! You definetly deserve more

I saw a similar question in SS Krotov, but in that question the wedge was at an inclination α with horizontal, and the hexagonal pencil made an angle φ from the plane of the incline. It asked the value of φ for which the pencil just stays in equilibrium. That question was interesting too

Great animations. I believe it will help me a lot in learning physics for Olympiads.

It's a really good question...me being in high school have learnt the concept of toppling in chapters like centre of mass and rotational dynamics..which were arguably helpful here

Man, the video is just MIND BLOWING. Every steps are so deeply explained.

Great video and explanation !!! Many more success to you .

Such a high-quality video and explanation!

Thank you for the video.. i was just going through some ipho papers and i saw the same problem but i didn't tried because i was developing my problems solving skills still developing .... But this video was great it was not very tough just didn't understood how 58% energy got lost after the impact🤔🤔.... Thank you anyways and please upload more 🙏

This is so awesome, your explanation is truly easy to grasp. Would love to see how you found out how much energy was lost each time.

The most underrated Physics Channel on KZfaq. You deserve more brother. De

Man everyone's getting recommended after he stopped uploading for 3 years.Its so random

This is so cooool, I seriously encourage you to do more tough IPHO problems, you are really good at it, well encouraged!

Please upload more videos! Subscribed to your channel from 3 devices already,mate! Consistency is key!!!

Dude please continue these videos. These are sooo good

Note that there will usually be some sliding if coefficient of friction isn't literally infinite. Also it can spontaneously transition to a runaway-accelerating hopping gate above a 24-27 degree angle, and maintain such a gate down to 14 degrees.

Very good quality... InsAllah,You can go further more.Doing such a good job.Love from Bangladesh.

Sir please make a video on the mathematical derivations concerned with the amount of energies lost. One of the best videos I've watched so far!

More reasons for why this first level of consideration is incomplete: * the materials in the game are plastic and elastic, so a pencil tipping over might see a noticeable return of energy. * the pencil not only has forward driving momentum, but it also has a rotational momentum (and this can be very strong). so in effect it can be the case that it will only shortly tip with its edges to the surface until it "floats" in air for the next edged to find contact. in other words, it does not necessarily fall down fast enough to just have at all any sort of flat contact with the surface. also air trapped might help it to get lifted quickly to such a "hovered" position. and guess what? a hovered motion will not have any sort (or at least much) of lifting up energy included - that would be able to stop a pencil from rotation. so the overall run length might be much increased. rationale: there might be much more in play that impacts on a real world setup. dont trust things to behave in a way the still simple formula above would predict.

4:26 Due to conservation of energy, with perfectly elastic collisions, the pencil should never stop rolling down no matter the angle if the pushing force is enough to tip it over once.

I actually saw this question a week or two and now I have the solution . Thank You , please keep this coming

Overclarified by the overthinking dude. You re an amazing explainer

Amazing video my dude. I want more from you.

Great Quality :) May u reach to millions !!

Brother love from India I am very amazed to see this that's the reason why I love physics ❤ Thanks for making such a video

subbed you deserve much more love

Very good content for so a small channel !!! , keep going and eventualy wont be small

I am a neet aspirant even tho I can understand by your simple explanation.... And I did completed the rotational motion chapter so I was connecting the chapter with the video.. Thank you❤

beauty of physics cannot be ignored

Before continuing the video I wanna write my initial guess of “anything greater than 30 degrees”. A hexagonal pencil has interior angles of 60 degrees on each angle. The pencil would perfectly balance on an edge at the center point of the angle, which is 30 degrees. At greater than 30 degrees, the pencil will no longer be stable, and fall towards the steep side. This will result in the pencil being unstable balancing on the next edge, causing it to fall to the side again. This would make the pencil role.

Wait... where did 58% come from?

I want to know how to find the exact amount of energy (In this case 58%) that is lost when the pencil collides with the surface while rolling down.

It's totally OK to include mathematical analysis in the videos too.

Alright I got 4 more years! So let's get started and Man You're Awesome Keep Up The Good Work !

I took the click bait designed to capture exceptional and brilliant mind’s attention. At the 9:23 mark of this fascinating video I awoke from a 90 second nap and thought. “This is rather interesting but I must have coffee to continue”. I have a rule (well one of very many) if I start watching a video and it has any merit at all I am obligated to hit the like button if by chance I die before coming back to it (I am a man who takes rules and duty very seriously and dying is on the table i’m 78). Just above the like button was the channel’s name “Overthinking Dude”. I laughed thinking well he does admit to this weakness as I admit to mine, For some very odd reason I believe what I think or write is worth the time to read (but most likely not) but you have gotten this far and I salute you. Your coffee is getting cold.

This channel needs more attention. You will probably not believe what happened. I solved thos question on the 1998 paper, was not sure what part (d) of the question (about limit of KE meant) so I asked my friend to explain the question. Then, a day after it was all done, he sends me this video. Quality content

More videos like this please❤

10:30 I don't quite understand why exactly 58% is lost

really interesting approach to solve the problem, it's a great video. ♥️

keep going dude! sincerely, an interested physics university student :D

Nice content brother 👌👏👍 continue and you will definitely be successful some day.

I enjoyed the presentation. Good to hear the physics reasoning and see the mathematical analysis. Combined, they provide a reasonable explanation of what we experience. Unfortunately, the problem and solution links don't work for me.

I remember trying to solve this problem :) This brings back memories! Nice

Amazing video! I'd love to understand how the recursion equation is solved by hand as I'm guessing graphing simulators wouldn't have been allowed at the Olympiad? Thanks!

A great content from a great channel

This is amazing! Wish you would solve some more IPho or other difficult problems :)))

insane presentation!!

Reminds me of one of my undergrad mechanical engineering courses about 60 years ago in kinetics and kinematics.

Amazing vid. I wonder tho... how the idea of rotational kinetic energy would affect this entire calculation. I reckon KE you give to the centre of mass is not just doing work to overcome the peak of potential energy and energy loss during a hit. But also to give the pencil it's rotational kinetic energy.!

Seriously your curiosity is just like anything

Why the energy lost in collision is 58%??

10:30 I don't understand where the 58% comes from. Does anyone know? Still, nice video.

I hope you make more contents!!! I like your videos.

Can you update the link in the description, it seems to be broken

Love this video! Question though, where did you get that 58% loss?

Not sure I understand you right, but don't we need to have both inequalities theta > 6.58° K_i > K_min (K_i = initial kinetic energy) for the pencil to at least start rolling and keep rolling?

There's something no one took into account. What material is he pencil made from ? And the table ? Depending on that, the pencil will roll before or after it's tipping point. So this exercice is void. Thanks to physics, you can save on brain power 👌🏻

Fantastic video!

Love it ❤thanx dear Do u use Manim for animation ?

Overthinking dude? Perfect name for me. Subscribed.

Thank god I found this channel

We need more of this and less of the dumb stuff we get suggest from KZfaq. Great analysis!

Real quality content

Amazing 💗

We did similar problems in my first year of engineering physics course. If it’s tilted where its center of mass is past any of its points of contact, then it tips- I think

Great content. Keep it going!

Great Video! Does someone know what tool os being used for Animation?

I want to see how you calculated that the pencil lost that procent of kinetic energy while he's falling down from his highest point, make the full-of-math video, please!!! I really like your video, thank you very much!

Beautiful!

Nice video bro!

You are a GOD SEND

Thank you).

Off course make the math for that, that’s why we’re here, also to be indulged by Mathematics equations, please 🙏

Hey man thanks!! Math is a great barrier for me please make that video with maths

The pencil colides with the pad in each step. If the colision is elastic, no energy is lost. That means, 58% is some serious guesswork. Also, the mass distribution doesn't matter, contrary to the claim at the end of the video, as long as mass is not movable and the center of gravity stays the same.

The first thing I thought when I saw this thumbnail is, the pencil is not perfectly hexagonal.

Amazing 👌

Roughly 58% is because the angular momentum is dependent on the pivot. The pivot changes when the next edge hits the table, so we "lose" a bunch of angular momentum. I think.

Great video buddy

how did u calculate the 58% thing???

Great video bro

Home-boy here pulled a gangsta 58 out of the back pocket and managed to smuggle in a calculator at an Olympiad. 10:30 . 17:13 . Show your work or get out. Also, solution "assumes" stuff at the end like Friction, drag, density. Give solution considering those variables or can I just "easily use a calculator" / LLM and send it?

At the 3:00 when the center of gravity is directly above point O, depending on the static friction, wouldn't the pencil start to slide? I know this is not the question being asked or the point of the video, I just thought it was an interesting argument that could be made for having a lower desk angle to maintain rolling if the rolling was initiated by external force.

Can't we apply the consepts of toppling and consider that when the vector that represents the weight of the pencil will cross one of the corner of the ground touching edge the pencil will topple and hence keep rolling...?

Great video!!

Hey awesome video man also could u tell me books or anything that u did to become a ipho medalist it would really help me a lot

There's a bit of an issue here. We are assuming that thehexagonal pencil is "walking" when rolling. That is, there is constant contact with the ground, and briefly there are two separate points of contact once every circumradius of the pencil. However, this will only be the case for a pencil that can make that sharp of an arc. That is, one where the vertical launch speed of the pencil can be cancelled within the time it takes to roll. Otherwise it will transition to either a very efficient running gate, or a less efficient bchaotic hopping/bouncing gate. The vertical launch speed of a pencil in a walking gate must be enough to reach 0 velocity at an apex of 0.134 circumradii under gravity within half a circumradius of horizontal travel. If we make the slightly wrong but helpful approximation that way the transition point the cycloidal arc is actually parabolic, for a 3.5mm radius, we get a time to apex of slightly under 9.8 milliseconds. This caps the step frequency of our walking gate at about 1 step per 19.6 ms, or a speed of 3.5 mm per 19.6 ms, or 178.9 mm/s. However, remembering that our steps are in fact cycloids and not parabolas, we end up with higher vertical velocity on every launch than necessary. This means that we will get too high an apex once our vertical speed ever exceeds approximately 96 mm/s. Which will actually happen at a speed of 166.3 mm/s. What we see is that we will transition to a running or hopping gate at somewhere around this speed. Basically once we reach about ~950 rpm it will either jump around like crazy or roll on the corners while being fully airborne at least some of the time. Which will actually occur is another question.

I'm kinda late but that was a pretty damn good video. I'm a chronic science tube content consumer