# Which body has high moment of inertia (rigid body or soft body)

I was reading explanation of why by spinning eggs on a table top,how will you distinguish a hard boiled eggs from a raw egg? In explanation it is given that Moment of inertia of raw egg is greater than boiled egg.

So do really moment of inertia of soft body is more than rigid body? How can I explain it? Is there any practical way to know about it(optional)?

• This is a biology question. The moment of inertia of a substance is given by: $$I = \int r^2 dm$$ We need to know how the matter inside the egg redistributes after it is boiled. – Yashas Feb 22 '17 at 14:28
• If you're talking about this type of experiment, the reason the experiment works is not that the moment of inertia changes in any appreciable way, but rather that the fluid inside the raw egg can rotate independently of the shell. – Michael Seifert Feb 22 '17 at 14:47

Moment of inertia $I$ is for rotation what mass $m$ is for linear motion. When spinning the egg, each bit that makes up this egg has a mass $m$ and is a distance $r$ form the centre of rotation. Each of these bits contributes to the total moment of inertia:

$$I=\sum r^2m$$

• When boiled you would expect a purely solid (gelly) content. Spinning the egg doesn't change the content considerably and so $I$ is constant.

• When unboiled you would expect a fluent content. Spinning the egg presses the inside up against the shell wall by centrifugal effect. It would make sense to assume more mass closer to the shell now, and so - according to the formula above - the bits now having on average a larger distance distance $r$ to the centre of rotation, increases the $I$.

• I think raw egg has less viscosity and boiled egg has high viscosity. So what do you think how it would effects moment of inertia of egg? – Fawad Feb 23 '17 at 12:29
• @Fawad 100 % viscosity is the same as saying "solid". The higher the viscosity, the more the content acts like my first bullet-point. – Steeven Feb 23 '17 at 13:08

The moment of inertia of a substance is given by

$$I = \int r^2 dm \tag{1}$$

The immediate conclusion you can infer from the above formula is that moment of inertia does not depend on the elasticity of the object, it only depends on the mass distribution.

Intuitively, the yolk (yellow part) is denser than the albumin (white part) of the egg. The albumin being a liquid allows the yolk to move around as the egg rotates. Therefore, the moment of inertia of an unboiled egg is variable.

When you rotate the egg, the centrifugal forces push the yolk towards the exterior. From equation $(1)$, you can claim that the moment of inertia of the egg increases. However, the albumin needn't necessarily move along with the shell. This would complicate the process. After a sufficiently long time, the albumin will move in sync with the shell. It is only here we can make a definite calculation of moment of inertia. Therefore, there could be a chance that the unboiled egg would make it to the bottom quicker than the boiled egg.

In the case of a boiled egg, the yolk cannot move around. The yolk is fixed to a particular position. The position of the yolk decides the moment of inertia. If the yolk is centered around the axis of rotation of the egg, the moment of inertia will be lower. If the yolk is at the walls of the egg, the moment of inertia will be higher.

There is no definitive answer to this question. It depends on the mass distribution of the contents of the egg.