Consider a body rotating about an axis passing through a point \\\\( O \\\\)and perpendicular to the plane of the paper. Let \\\\(P\\\\) be the position of a particle inside the body. If the body rotates through an angle \\\\( 0 \\\\) in a time interval of \\\\( t \\\\), the particle at \\\\(P\\\\) reaches \\\\(P ' \\\\) \\\\( \ herefore \\\\) Linear displacement \\\\(PP' =r \ heta \\\\) \\\\( \ herefore \\\\)Linear velocity, \\\\( v=\\dfrac{PP'}{t}=\\dfrac{r \ heta}{t } \\\\)But \\\\( \\dfrac{\ heta}{t}=\\omega \\\\), the angular velocity\\\\( \ herefore \\\\)Linear velocity , \\\\( v=r \\omega \\\\)