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)

h_{1} and b_{1} are constants.

b_{2} depends on h_{2}

d(h_{2}) is:

equ. (3)

In equ. (3) there is a limited range of h_{2} that yields a real solution.

d is maximized when h_{2} goes to zero.

This corresponds to an infinitely long, infinitely thin rectangle.