Whirlda: Euler's Disk
Mechanics, Chaos & Fluids arc, page 93 of 193. Back to The Pixelated Physics Universe
Who they are
Whirlda's tilted shield sinks lower and rings faster, until it stops dead.
Whirlda is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Spin a heavy disk on a flat table. As it loses energy and leans lower, its wobble speeds up, then it stops dead in a finite time. For a small tilt, rolling without slipping, the wobble rate rises as the tilt falls. Moffatt's 2000 model blamed air drag, but vacuum tests and rolling-friction models disagree on the cause.
$$ \begin{gathered} \Omega \propto \alpha^{-1/2} \\ \text{Moffatt (2000), air drag: } \alpha \propto (t_0-t)^{1/3} \;\Rightarrow\; \Omega \propto (t_0-t)^{-1/6} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\Omega$ | angular speed of the contact point round the table | rad/s |
| $\alpha$ | tilt angle between disk face and table | rad |
| $t$ | time | s |
| $t_0$ | finite stopping time | s |
Honest caveat: The exponent is still debated. The wobble never reaches infinite speed: real contact physics takes over first.
Status: part of this topic is unsolved, unconfirmed or debated. The text above says which part; treat it as an open question, not settled fact.
Sources
- Moffatt (2000) Euler's disk and its finite-time singularity, Nature 404, 833
- Easwar, Rouyer & Menon (2002) Speeding to a stop: The finite-time singularity of a spinning disk, Phys. Rev. E 66, 045102
- Le Saux, Leine & Glocker (2005) Dynamics of a Rolling Disk in the Presence of Dry Friction, J. Nonlinear Sci. 15, 27
Crossovers
Whirlda meets Celtrix (Rattleback). Celtrix and Whirlda are both rigid bodies on a table where friction at the contact point matters. Celtrix's twisted mass axes turn wobble into reversed spin; Whirlda's dissipation makes her wobble speed up until she stops.
Whirlda meets Sloshwyn (Coffee Sloshing Resonance). Sloshwyn's coffee rings down as damping takes its energy. Whirlda loses energy too, but as she does, her wobble rate rises, heading toward a finite-time singularity that real contact physics cuts off before it arrives.
Wear the lore
Concept keywords: Euler's Disk, Whirlda, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics