I assume the capacitor plates have a fixed charge.
As the conductor rotates, the capacitance between the plates will be changed. With the conductor parallel to the plates, the capacitance will be that of a parallel plate capacitor. With the conductor perpendicular to the plates, the capacitance will be slightly higher because the plate separation will be less near the conductor.
Capacitance is defined by; C = Q / V ; so V = Q / C ; dv = Q / dc .
The plate voltage will therefore change as the conductor rotates, because the plate capacitance changes. The voltage change will be an asymmetric ripple, at twice the rotation frequency, subtracted from the initial plate voltage.
The conductor will be reversed twice by each rotation, so the charge distribution induced on the surface of the conductor must alternate. An alternating current will therefore flow in the conductor, which has become a dipole antenna in an alternating electric field.
To extract energy from the dipole, terminals would NOT be connected to the ends of the dipole conductor, rather the dipole would be cut at its midpoint, where a low impedance two wire transmission line would be connected. The energy extracted by that line, would tend to oppose the mechanical rotation of the dipole.
That is only a first order analysis. Currents and voltages will change in magnitude and phase as energy is extracted.