Question #42828

An electric dipole of dipole moment $p$ (in $\text{C}\cdot\text{m}$) is constrained to rotate in the $xy$-plane about a fixed pivot at the origin. A frictionless mechanism alters the mass distribution of the dipole assembly such that its moment of inertia about the pivot depends on its angular position $\theta$ (the angle between the dipole moment and the positive $x$-axis) as $I(\theta) = I_0 (1 + \alpha \sin^2\theta)$, where $I_0$ (in $\text{kg}\cdot\text{m}^2$) and dimensionless $\alpha$ are positive constants. The mechanism is fixed to the ground and does no net work, ensuring the mechanical energy of the assembly is conserved. A uniform electric field $E$ (in $\text{N/C}$) exists along the positive $x$-axis. If the assembly is released from rest at $\theta = \pi/2 \text{ rad}$, what is the magnitude of its angular acceleration (in $\text{rad/s}^2$) when it passes through $\theta = \pi/4 \text{ rad}$?