Physical meaning of Radius of Gyration

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The Radius of Gyration (Rg) is a key property in polymer science, representing the average distance of mass points in a distribution from a specific axis, which relates to the moment of inertia. It allows for the comparison of mass distributions of different polymers, providing insights into their structural properties. The Rg value can indicate how the mass is spread out in relation to an axis, affecting the material's mechanical behavior. Understanding Rg is crucial for predicting the performance of polymers in various applications. Overall, Rg serves as a significant metric for evaluating and comparing the physical characteristics of polymers.
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Out of many properties polymer scientists are interested to calculate one of the most common is "Rg" i.e. Radius of Gyration. Can anyone put more light on the physical significance of this value?

Can Rg value of two polymers be compared? If yes what conclusion can be drawn from such comparison?
 
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For a mass distribution of a rigid body we can calculate the moment of inertia of that mass distribution about any axis (around it- [within it as well]). The moment of inertia differs for the same mass taken through different axes.

Suppose we have calculated the moment of inertia of a mass distribution through an axis. So radius of gyration is such an arbitrary distance from the given axis at which a point mass of the same mass (as the given mass distribution) can be supposed to have stayed so that it would give same moment of inertia as the mass distribution.

So basically radius of gyration is "average" of distances of each point mass in a mass distribution.

[My "average" here is not arithmetic mean or geometric mean ...]
 

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