on . Posted in Classical Mechanics Radius of gyration, abbreviated as k or r, also called gyradius, is used in physics and engineering to describe the distribution of mass or the spatial extent of an object around an axis of rotation.  It is a measure of how the mass is distributed or how the object's mass is spread out from the axis of rotation.  In simple terms, the radius of gyration represents the effective distance from the axis at which the mass of an object is concentrated.  It is similar to the concept of the center of mass but provides information about the distribution of mass in relation to the axis of rotation.

The moment of inertia represents the object's resistance to changes in rotational motion and depends on the mass distribution and the shape of the object.  The radius of gyration, therefore, provides a convenient way to describe the mass distribution and rotational characteristics of an object without the need to consider its specific shape.

$$\large{ k = \sqrt{ \frac{ I }{ A_c } } }$$     (Radius of Gyration)

$$\large{ I = k^2 \; A_c }$$

$$\large{ A_c = \frac{ I }{ k^2 } }$$

### Solve for k

 seconc moment of area, I area cross-section, Ac

### Solve for I

 adius of gyration, k area cross-section, Ac

### Solve for Ac

 second moment of area, I radius of gyration, k

Symbol Metric Metric
$$\large{ k }$$ = radius of gyration $$\large{ in}$$ $$\large{ mm}$$
$$\large{ I }$$ = secont moment of area $$\large{ in^4}$$ $$\large{ mm^4}$$
$$\large{ A_c }$$ = area cross-section of material $$\large{ in^2}$$ $$\large{ mm^2}$$

## Radius of gyration x/y axis Formula

$$\large{ k_x = \sqrt{ \frac{ I_x }{ A_c } } }$$

$$\large{ k_y = \sqrt{ \frac{ I_y }{ A_c } } }$$

Symbol Metric Metric
$$\large{ k_x }$$ = radius of gyration x-axis $$\large{ in}$$ $$\large{ mm}$$
$$\large{ k_y }$$ = radius of gyration y-axis $$\large{ in}$$ $$\large{ mm}$$
$$\large{ I_x }$$ = secont moment of area x-axis $$\large{ in^4}$$ $$\large{ mm^4}$$
$$\large{ I_y }$$ = secont moment of area y-axis $$\large{ in^4}$$ $$\large{ mm^4}$$
$$\large{ A_c }$$ = area cross-section of material $$\large{ in^2}$$ $$\large{ mm^2}$$ Tags: Moment of Inertia