Can you prove this statement Mathematically?

Question

You can spin the egg. Since viscosity is a measure of a liquid's resistance to shear forces, seeing how the egg resists spinning (or continues to spin after you stop it) will tell you something about its viscosity. A thin yolk will continue to spin after you stop it because the inner yolk continues to spin even though the outer layers are stopped. As the inner yolk spins, it applies a shear force to the outer layers, which eventually cause the egg to spin again. A very viscous yolk (say, a hard boiled egg) resists shearing altogether, and the inner yolk stops when you stop it, so there is no spinning afterwards.

Answer 1

Yes. You can approximate the equation of motion of the yoke as:

d^2Y/dt^2=A*(dY/dt-dS/dt)

t is time, Y is angle of yoke, S is angle of shell, and A is the viscous coupling constant. Details left to reader.

Answer 2

♠ well, lemme try! Maths implies formulas. Correct formulas may be based on goodly idealized model of reality. I don’t pretend on quantitative correspondence, qualitative analysis will do;
♣ my model is: suppose a solid cylinder A (for yolk) of radius r, suppose a hollow cylinder B (for white + shell) of outer radius R and inner radius r, so they fit snug and some friction is present, friction being supposed to substitute viscosity; now we start rotating B with angular speed w, and sooner or later A should also rotate with w;
♦ now we grip B for a tiny time enough to stop it and release it at once; here we may compose an equation of motion for both cylinders that looks: etc, etc, etc on;
ready to continue by yourself? If not click me for further speculations;
♥ with some parameters procured experimentally the model must work; the only flaw I see here by now, the model does not take into account the umbilical cord between yolk and white of the egg, that would result in oscillatory motion herewith.

Answer 3

This is a difficult question.