Torques Based on Gear Radii  
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Two gears A and B are connected. A is larger than B. A counter clockwise arrow indicates T subscript small on gear B. An upward force F is applied on B at the connecting teeth of A and B. F = T subscript large over R subscript large.

Next, consider the FBD for the small gear.

The large gear exerts an equal and opposite force F on the small gear. The rotation caused by force F will be resisted by a torque applied to the small gear by shaft B.