Why is radius of gyration important

They have the same value because the radius is constant. You do not have the Flash plugin. Radius of gyration r This is another property of a section and is also a function of the second moment of area. The diagram indicates that this member will bend in the thinnest plane. The formula for the radius of gyration r is:. It even find its applications in polymer physics where the radius of gyration is used to describe the dimensions of a polymer chain wikipedia.

Radius of gyration also have mathematical definition. Radius of gyration generally shows up in two places: Strength of materials: Here two dimensional radius of gyration is used and is defined as area property.

Area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. This variation finds its applications in engineering Area Moment of Inertia.

In this case it is defined as mass property. From above explanation we can see that in both the cases radius of gyration means different things i. Since we would be studying it in rotational mechanics where we are studying the rotation of objects around a fixed axis of rotation we will only study radius of gyration in context to mass moment of inertia.

Having decided which radius of gyration we have to study here let us now learn about gyradius in detail. When a body or an object is having translational motion the inertia of the body depends only on the mass of the body. In case of rotational motion , moment of inertia depends on two factors mass of the body effective distance of its particles from the axis of rotation.

This means that moment of inertia depends on the mass distribution about the axis of rotation. Radius of gyration of a body is defined about the axis of rotation of the body. Gyradius Definition: The radius of gyration of a body about its axis of rotation may be defined as the distance from the axis of rotation at which, if the whole mass of the body were concentrated and its moment of inertia about the given axis would be the same as with the distribution of mass.

So, Whatever may be the shape of the body it is always possible to find a distance from the axis of rotation at which whole mass of the body can be assumed to be concentrated and even then its moment of inertia about that axis remains unchanged.

Thus, the radius of gyration of a body, rotating about a given axis of rotation is the radial distance from the axis and when the square of radius of gyration k is multiplied by the total mass of the body it gives the moment of inertia of the body about that axis.

Let us now again look at the definition of radius of gyration from mathematics point of view.