Question

Relation between radius of gyration and moment of inertia

Answer 1

Hello mate,

Here is your answer,

We know the basic formula for moment of inertia of a rigid body is $m {r}^{2}$

$m {r}^{2} \\ \\ r = k \\ \\ (k \: \: is \: radius \: of \: gyration) \\ \\ i = m {k}^{2} \\ \\ {k}^{2} = \frac{i}{m} \\ \\ k = \sqrt{ \frac{i}{m} }$

Hope it helps:)

Answer 2

When a torque is applied to an object it begins to rotate with an acceleration inversely proportional to its moment of inertia. This relation can be thought of as Newton's Second Law for rotation. The moment of inertia is the rotational mass and the torque is rotational force. Angular motion obeys Newton's First Law.