#### 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 $$P ' $$

$$ \therefore $$ Linear displacement $$PP' =r \theta $$

$$ \therefore $$Linear velocity, $$ v=\dfrac{PP'}{t}=\dfrac{r \theta}{t } $$

But $$ \dfrac{\theta}{t}=\omega $$, the angular velocity

$$ \therefore $$Linear velocity , $$ v=r \omega $$