Mean Square Distance from the Center of Gravity

3 Mean Square Distance from the Center of Gravity 

The equation that defines a center of gravity is shown in Fig. 1.29. The sum of the vectors from the center of gravity to all elements of the object (assumed to be of equal mass) is zero. The figure shows the correlation of the vectors from the center of gravity of a macromolecule to the end-to-end vectors. The equation for the mean square distance from the center of gravity is illustrated, but not derived. The sums 

Mean Square Distances Between the Ends and From the Center of Gravity 

The density of matter within the random coil is a quantity that lets one better understand the nature of macromolecules. The overall conformations is also called the macroconformation (see Fig. 5.42). The density of a given molecule in a random coil macroconformation can be estimated by assuming that the coil locates in a spherical volume V with a radius of its root-mean-square end-to-end distance. Taking the example of the standard polyethylene of the previous section of molar mass 280,000 Da (4.65x10 kg molecule ) and 1 = 21.8 nm, one finds that 

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