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Considering the Fig. 8.3,

Transfer of Axis” = C

Suppose AB and CD are two parallel lines. AB passes through any point P of a rigid body and CD passes through its centre of mass, G.

From trigonometry, we get the calculation as-

r2G + d2 +r2/ 2rG d

 = r2G + d2 +r2/ 2rG d

2r2G+ d = r2G + d2 – r2

r2 = r2G + d2 + 2rGd

Now,

I = 2dm

  = 2G + d2 + 2rGd } dm

  =2Gdm + d22Gdm

  = IG + d2m + 2d dm

  = IG + md2 + 0                                                (Since, dm = 0)

Hence,

I = IG + md2

Similarly, we can calculate,

K2 = K2G + d2

Where,

KG is the Radius of Gyration