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For mechanical stability - you want the object to remain in its place without moving:

1) The sum of all forces on the object must be zero. If this is not the case, the object will accelerate.

2) The sum of al torques on the object must also be zero. For example, forces that add up to zero, but that pull or push on differents part of the object, may make it rotate.

For actual calculations, this can be separated into component form, three equations for part (1), and another three equations for part (2).

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