What is radius of gyration ? please explain ith examples.
Radius of gyration of a body about a given axis is the perpendicular distance of a point from the axis, where if whole mass of the body were concentrated, then the body shall have the same moment of inertia as it has with the actual distribution of mass. This distance is represented by K. The momentum of inertia of a body of mass M and radius of gyration K is given by,
Since, the r adius of gyration of a body is defined about its axis of rotation it will change if we change the axis of rotation of the object.
1) The moment of inertia of a ring about an axis passing through its center of mass and perpendicular to plane of ring is given by, I = MR2
Where, M = mass of the ring, R = radius of the ring
So, the radius of gyration 'K' can be found as,
MR2 = MK2
=> R = K
2) The moment of inertia of a ring about its diameter is given by,
I = (1/2) MR2
So here the radius of gyration is,
MK2 = (1/2) MR2
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Radius of gyration is the root mean square distance of the objects ' parts from either its center of gravity or an axis.
One way to think of it is that the object 's moment of inertia is equal to that of a point mass at a distance of the radius of gyration from the axis.
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