what is Radius of Gyration?
Answers
Answer:
Moment of Inertia is defined as the rotational analog of Mass.
In simple terms, in Linear motion we expressed an object as mass while in rotational motion we express an object as Moment of Inertia.
We can denote Moment of Inertia as Mass × Radial Distance.
Here the radial distance is the distance from the axis to the point where Rotational Force is applied. Different objects have different Moment of Inertia.
Example:
- MOI of Solid Sphere = 2/5 MR²
- MOI of Thin Rod at the centre = ML²/12
- MOI of Ring = 1/2 MR²
On Analyzing the above examples we can see that, Moment of Inertia depends only upon two things, Mass and Radial Distance along with some constant numerical terms. Therefore in General Form we can write MOI as:
⇒ MOI = M × K²
Where, K is the Radius of Gyration.
Radius of Gyration is defined as the Radial distance from the axis to the point where the force is applied. This force results in rotational motion and Moment of Inertia for that object. In Mathematical Terms, Radius of Gyration is written as:
⇒ I = MK²
⇒ K² = I/M
⇒ K = √ ( I/M )
Answer:
Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance of a point ,from the axis of rotation at which, if whole mass of the body is assumed to be concentrated, its moment of inertia about the given axis would be the same as with its actual distribution of mass.
The radius of gyration is used to compare how various structural shapes will behave under compression along an axis. It is used to predict buckling in a compression beam or member.