A Simple Problem on the Hardest Physics Olympiad (IPhO)

In this video, we find the smallest angle of inclination that allows a common pencil to roll indefinitely given a small initial push.

The Problem:

The Solution:

[gnnvoauekes]

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

[thakyou]

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.

[akshitkumar]

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

[yaminocrow]

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

[IntegralKing]

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

[dontmesswiththeriddim]

Damn, Youtube 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!

[matheuspauloferreira]

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

[INSP_NITIN]

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

[petersmythe]

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.

[PARADOX-kh]

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

[bobogirraffe]

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

[soumakbhattacharjee]

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

[Inndjkaawed]

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?

[himeshviews]

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

[vanshjhunjhunwala]

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

[NeatNit]

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

[godfxth]

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

[ahmedsaadsabit]

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

[namangoyal]

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

[AalapShah]

I didn't watch the full video but found the problem quite intriguing after the point where he says it's not 30°. So I searched for 1998 physics olympiad and found the question paper. And I must say it's designed so nicely that the 5 sub-questions subtly nudge you towards the final solution. I haven't solved many physics problems for 5-7 years now, but I could solve it in a couple of hours because of all the sub-questions guiding me in the right direction. It felt very satisfying to solve it myself and I must say I wouldn't have been able to do it if the questions weren't framed so beautifully.