There's an arm of length l and mass m, and a motor-driven shaft with a constant torque t.
The arm swivels on a fixed pivot point.
The strategy on the left uses a cable anchored on the far end and the cable is spooled by turning the shaft clockwise to move the arm to a certain angle. The movement happens linearly, deg/s degrees per second.
The setup on the right uses a gear welded onto the pivoting end of the arm. Keeping every other trait of the system the same, how can I resolve the necessary gear ratio to move the arm to the same angle at the same deg/s?
(Motors in both systems should draw equal power from the wall)