# 2.4: Radius of Gyration

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- 6935

[ "article:topic", "radius of gyration", "authorname:tatumj", "showtoc:no" ]

The second moment of inertia of any body can be written in the form \(mk^2\). Thus, for the rod, the disc (about an axis perpendicular to its plane), the triangle and the disc (about a diameter), \( k\) has the values

\(\dfrac{l}{\sqrt{3}} = 0.866l, \dfrac{a}{\sqrt{2}} = 0.707a, \dfrac{a}{\sqrt{6}} = 0.408a, \dfrac{a}{2} = 0.500a\)

respectively.

\( k\) is called the **radius of gyration**. If you were to concentrate all the mass of a body at its radius of gyration, its moment of inertia would remain the same.