Equilibrium Equations  
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Diagram shows a vertical shaft centered on the x prime axis which is twisted to the left with a gear marked C on the top end. The radius of the gear C is D subscript C over 2 and the diameter is 100 millimeters. A force F is acting vertically upwards on the circumference of the gear C from the bottom left. An internal torque T subscript 2 is applied on the post vertically downwards along the shaft.

The moment equilibrium for gear A and shaft (1) is:

Draw a FBD around gear C, cutting through shaft (2). Assume a positive torque T2 in shaft (2).

The teeth of gear A exert an equal magnitude force F in the opposite direction on gear C.

The moment equilibrium for gear C and shaft (2) is:

Note: There are three unknowns (T1, T2, and F) but only two equations.