Assumptions: The weight of the antenna is a point-load at the center of mass of the antenna (1.12 meters), the antenna is supported on one side, and the beam is made from pure aluminum 6061.

Beam deflection: Hand-calculations:

Beam deflection: Calculated using FEA in Solidworks.

The maximum beam deflection at the center of mass, as calculated by SolidWorks, is 2.23 cm, matching the hand calculations.
Required torque: The torque to rotate the antenna on its axis approaches zero as the rotation becomes slower. At a speed of 1 degree per minute, the torque required to spin the antenna radially is effectively zero.
Therefore, the only source of significant torque is due to the beam deflection, which off-sets the center of mass of the antenna, resulting in torque due to gravity.
