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Radius of Gyration Definition

Formula | Transfer of Axis
 
Area Radius of Gyration Definition
The Radius of Gyration of an Area about a given axis is a distance k from the axis. At this distance k an equivalent area is thought of as a line Area parallel to the original axis. The moment of inertia of this Line Area about the original axis is unchanged.
Mass Radius of Gyration Definition
The Radius of Gyration of a Mass about a given axis is a distance k from the axis. At this distance k an equivalent mass is thought of as a Point Mass. The moment of inertia of this Point Mass about the original axis is unchanged.
Radius of Gyration Concept
Figure 1
It is possible for two EQUAL areas to have equal MOMENT'S OF INERTIA about the same axis while having different dimensions.
Figure 1 contains two rectangles. Setting the Area's and Moment's of Inertia equal, the following relationships can be found.
equ. (1)
equ. (2)
h1 and b1 are constants.
b2 depends on h2

d(h2) is:
equ. (3)

In equ. (3) there is a limited range of h2 that yields a real solution.

d is maximized when h2 goes to zero.

This corresponds to an infinitely long, infinitely thin rectangle.

The maximum value of d is the Radius of Gyration.

equ. (4)
This is equivalent to using the general Radius of Gyration equation on a rectangle.
The mass Radius of Gyration is the same concept just applied to a mass.