Radius of Gyration
Tags: Moment of Inertia Equations
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.
Radius of gyration Formula 

\(\large{ k = \sqrt{ \frac{ I }{ A_c } } }\) (Radius of Gyration) \(\large{ I = k^2 \; A_c }\) \(\large{ A_c = \frac{ I }{ k^2 } }\) 

Solve for k
Solve for I
Solve for Ac


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 crosssection 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 xaxis  \(\large{ in}\)  \(\large{ mm}\) 
\(\large{ k_y }\) = radius of gyration yaxis  \(\large{ in}\)  \(\large{ mm}\) 
\(\large{ I_x }\) = secont moment of area xaxis  \(\large{ in^4}\)  \(\large{ mm^4}\) 
\(\large{ I_y }\) = secont moment of area yaxis  \(\large{ in^4}\)  \(\large{ mm^4}\) 
\(\large{ A_c }\) = area crosssection of material  \(\large{ in^2}\)  \(\large{ mm^2}\) 
Tags: Moment of Inertia