Angular velocity \(=\frac{v_n}{r_n}\)

Product of angular velocity and tangential velocity \(=\frac{v_n}{r_n} \times v_n\)

or \(\frac{v_n^2}{r_n}\)

or \(\frac{v_0}{r_0 n^4} \quad\left(\because v_n=\frac{v_0}{n}\right.\) and \(\left.r_n=n^2 r_0\right)\)

Hence product \(\propto \frac{1}{n^4}\)