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’.
∴ Linear displacement pp' = r θ
∴ Linear velocity, v = (pp'/t) = rθ/t
But θ/t = ω, the angular velocity
∴ Linear velocity, v = r ω.
