Applied Mechanics and Graphic Statics
The resultant of the forces acting on a body will be zero if the body

Moves with variable velocity in a straight line
Does not move at all
Moves along a curved path
Rotates

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Applied Mechanics and Graphic Statics
If a set of given forces are such that their free vectors build a closed polygon, then

The resultant force is zero but resultant couple may not be zero
The resultant force is zero but resultant couple is not zero
The resultant force and resultant couple both may not be zero
The resultant force and resultant couple are always zero

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