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Old 07-01-2008, 06:17 AM   #17 (permalink)
ttoyoda
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To solve a statics problem, the sum of all the forces AND torques must be zero.
So there must be a force to offset or balance the force on the spring scale. This force is the red arrow marked REACTION FORCE on the diagram. This force must be equal in magnitude to the spring scale force but opposite in direction.

If we choose the center of the motor shaft as the pivot point for the torque calculations it makes things easy, because the lever arm length is the same for both the spring scale and the reaction force. Adding the two values gives a result that is twice what was measured on the spring scale. Alternately we could have chosen the point at which the motor touches the table as the zero point, in this case the spring scale force would be as measured but the lever arm would have doubled in length. Both solution methods give the same result. So either way, the torque on the fan/motor is twice what was initially calculated.

Statics problems are rich in opportunities to make errors. Hopefully I have not made one here.
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