hello aspirant

the moment of inertia of a body about an axis is sometimes represented using the radius of gyration i.e it is the imaginary distance from the centroid at which the area of cross section is imagined to be focused at a point in order to obtain the same moment of inertia. It is denoted by k .

yes we can measure the radius of gyration by the following method:

The formula of moment inertia in terms of the radius of gyration is given as follows:

I = mk ² (1)

where I is the moment of inertia and m is the mass of the body

Accordingly, the radius of gyration is given as follows

k=Im−−√ (2)

The unit of radius of gyration is mm.

Consider a body having n number of particles each having a mass of m . Let the perpendicular distance from the axis of rotation be given by r ₁ , r ₂ , r ₃ ,…, r _n . We know that the moment of inertia in terms of radius of gyration is given by the equation (1). Substituting the values in the equation, we get the moment of inertia of the body as follows

………… (3)

If all the particles have the same mass then equation (3) becomes

We can write mn as M which signifies the total mass of the body. Now the equation becomes

………… (4)

From equation (4), we get

From the above equation, we can infer that the radius of gyration can also be defined as the root mean square distance of various particle of the body from the axis of rotation. It is used to compare how various structural shapes will behave under compression along an axis.

hope this helps