Question

Why is it useful to define the radius of gyration?

Answer 1

Hint: Radius of gyration is related to moment of inertia. To understand the radius of gyration we should have knowledge about the moment of inertia. Moment of inertia is different from momentum.

Complete step by step answer
Radius of gyration is defined as the distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated about an axis of rotation
Radius of gyration about the axis, equal to the square root of the quotient of the moment of inertia and the mass.
It is given by the expression,
Where,
K is the radius of gyration
I is the moment of inertia
m is the mass
The unit of the radius of gyration is millimetre
The radius of gyration is used to compare structural shapes and how they will behave under compression along an axis. It is used to predict buckling in a compression beam.
The physical significance of defining the radius of gyration is as follow,
The radius of gyration is a measure of distribution of mass about the given axis of rotation.
If the particles of the body are distributed close to the axis of rotation, the radius of gyration is less and if the particles are distributed away from the axis of rotation, the radius of gyration is more.
The mass and radius of gyration of the body about a given axis of rotation gives the value of its moment of inertia about the same axis, even if we do not know the actual shape of the body.

Note: If an object has mass, then it will have mass moment of inertia. And the magnitude of the inertia will depend on the chosen axis of rotation. Therefore, if an object has inertia, you can calculate the radius of gyration using the discussed formula.