Radius of Gyration Definition
| Formula | Transfer of Axis |
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| 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. | |||
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| 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. | |||
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| 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. | |||
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equ. (1) | ||
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equ. (2) | ||
| h1 and b1 are constants. | |||
| b2 depends on h2 | |||
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d(h2) is: |
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equ. (3) | ||
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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. |
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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. | |||
