Find the Bad Egg (Through Physics!)

When watching a “kitchen hacks” video on instagram I saw a quick way to test if an egg is hard boiled or raw (I know, definitely a useful solution for all the times I forget if I’ve boiled my egg or not). The gist of the hack was that if you place an egg of questionable content and spin it it will spin fast and steady if hard boiled whereas if it is raw it will spin very slowly while wobbling and then stop. This interesting phenomena can in part be explained by physics, specifically rotational inertia. The raw yolk of an egg is more dense than the raw egg whites, so when placed on its side the yolk sits towards the bottom. This means, that more mass is concentrated towards the bottom of the egg, adjusting its center of mass away from the eggs center. The hardboiled egg on the other hand has an even distribution of mass throughout the egg.   

The egg is being spun by a torque perpendicular to the red line shown. The eggs- while they are the same shape and mass have different moments of inertia due to their different distribution of mass. The hard boiled egg has a smaller radius relative to the point of the egg that the torque is applied. This results in the hard boiled egg having a smaller moment of inertia than the raw egg. This means, if similar amounts of torque are applied to a hard boiled and a raw egg, the hard boiled egg will have a faster angular acceleration, and will spin faster. 

τ = Iα