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प्रश्न
Answer in brief:
Why is it useful to define the radius of gyration?
उत्तर
Definition: The radius of gyration of a body rotating about an axis is defined as the distance between the axis of rotation and the point at which the entire mass of the body can be concentrated to give the same moment of inertia as that of the body about the given axis.
The moment of inertia (MI) of a body about a given rotation axis depends upon (i) the mass of the body and (ii) the distribution of mass about the axis of rotation. These two factors can be separated by expressing the MI as the product of the mass (M) and the square of a particular distance (k) from the axis of rotation. This distance is called the radius of gyration and is defined as given above. Thus,
I = `sum_"i""m"_"i""r"_"i"^2 = "Mk"^2`
∴ k = `sqrt("I"/"M")`
The pressure applied at a specific location can be determined with the use of the radius of gyration. When calculating the strength and intensity between specified cross-sections of a region, it is highly helpful. The radius of gyration for a given point decreases with increasing distance from the rotational axis.
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