Physics Olympiad: Finding the Terminal Velocity of a Pencil | IPhO 1998 pr1 & Morin 8.66

This difficult physics problem is from the international physics olympiad (IPhO) (hardest), though in 1998, and I also modified it for this video. It looks at a pencil, hexagon, rolling down an inclined plane/a hexagon rolling down an inclined plane. It is quite an elegant mechanics problem looking at the terminal velocity of a hexagon rolling down an inclined plane, it is not such a common setup of high school physics. Many physics olympiad problems are tricky and elegant in this matter which makes physics olympiads so fun.

This sort of problem is relevant to JEE, F=ma, USAPhO (USA physics olympiad), IPhO (international physics olympiad), CPhO, NBPhO, and many other physics olympiads. Of course the tid bits of geometry are also relevant to competitions like AMC, AIME, etc. Though this isn't a how to win a gold medal at USAPhO/IPhO/qualify for F=ma, it can give you problem solving strategies that would help you with those.

We use properties of hexagons, conservation of angular momentum, conservation of energy, and an idea about terminal velocity to solve this problem. These yield a much nicer method of approach than using things such as forces.

This video was made with manim from 3Blue1Brown.

Sources:
https://scholar.harvard.edu/david-mor...
https://www.ioc.ee/~kree/students/iph...