Apply classical mechanics to an electron in a stationary state of hydrogen to show that $L^{2}=m_{\mathrm{e}} k e^{2} r$ and $L^{3}=m_{\mathrm{e}} k^{2} e^{4} / \omega .$ Here $k$ is the Coulomb constant, $L$ is the magnitude of the orbital angular momentum of the electron, and $m_{\mathrm{e}}, e, r,$ and $\omega$ are the mass, charge, orbit radius, and orbital angular frequency of the electron, respectively.