Question #42757

A rigid symmetric dipole is modeled as a symmetric top with moment of inertia $I_3$ about its symmetry axis and $I_1$ about any transverse axis passing through its center of mass. The dipole has a permanent electric dipole moment $\vec{p}$ directed along its symmetry axis. It is placed in a uniform electric field $\vec{E}$ directed along the positive Z-axis. Initially, the symmetry axis of the dipole is held at an angle $\theta_0 = 60^\circ$ with respect to the Z-axis. The dipole is given an initial spin angular velocity $\omega_3$ about its symmetry axis such that $\frac{I_3^2 \omega_3^2}{I_1} = \frac{7}{2} p E$ (where $p = |\vec{p}|$ and $E = |\vec{E}|$), and then released such that its initial nutation and precession angular velocities are zero. Find the maximum magnitude of the precession angular velocity $|\dot{\phi}|_{\text{max}}$ (where $\phi$ is the azimuthal angle around the Z-axis) of the dipole during its subsequent motion. Assume no non-conservative forces are acting on the system.