What is radius of gyration?

please tell me in simple words.......i find hard to understand

1 Answer
Jan 6, 2018

see below

Explanation:

enter image source here

consider the two diagrams above

In diagram 1 we have a shape rotating about an axis. If the mass is#m#

then its moment of inertia is

#I=mr^2#

in diagram 2 we have the same axis of rotation but this time the same mass is concentrated at a point.

its moment of inertia is

#I'=Mk^2#

if the two values of the moments of inertia are the same

then #k# is called the radius of gyration#

in other words the radius of gyration is the distance from the axis of rotation at which the total mass of a body is assumed concentrated and at which the moment of inertia will be equal to the actual moment of inertia of the body.

so

#I=Mk^2#

#:.k=sqrt(I/M)#