Mechanics principle When two forces of equal magnitude, opposite in direction and parallel act on an object, the object will rotate without having translational speed. 
On the other hand, when three concurrent forces acted on an object so that they cancel each other out, the object will not have translational velocity. 


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*However, in this case will the object rotate or not? 

*How do we know it? 

*Should we consider the moment with each point being the pivot?
 A: 
When two forces of equal magnitude, opposite in direction and parallel act on an object, the object will rotate without having translational speed.

This condition is not enough. In rotational mechanics the position is also important.
The point that makes this simple to overview is, that


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*changes in translational motion is described by forces and e.g. through Newton's 2nd law $\sum F=ma$ for any direction

*changes in rotational motion is described by torques and e.g. through an analogue of Newton's 2nd law $\sum \tau=I\alpha$ for any rotation axis.


And torques are calculated from a force and its position.
You conclude that translational motion doesn't change, because forces are equal in opposite directions. So $\sum F=0$. If there were three forces, this is still the method.
Same goes for rotation.
For example: If the two forces act along the same line, then they try to turn the object opposite ways with equal torque. For example, one pull up on the right side while the other pulls down also at this point on the right side. Nothing happens. If they instead act on either side of the rotation centre, then they will turn the object the same way, since on the right side one pulls up and on the left side one pulls down, and the object will turn.
When three forces act, the same applies. Each of them causes a torque $\tau$:
$$\tau=Fr$$
where $F$ is the perpendicular force component and $r$ the distance from the point where the force acts to the centre. To have things not rotating, angular acceleration $\alpha$ must be 0, so the simple requirement is from the analogue of Newton's 2nd law above:
$$\sum \tau=0$$
First find all forces. Then calculate all torques caused by these forces. Then sum them. If the sum is zero, the rotation doesn't accelerate.
This will work for a 1d case (around one axis). For a 2d or 3d case, all forces just have to be split in their components that act around the different rotation axes and then the above sum is done for all 3 different axes.
