torque on a body without any supporting point Suppose there is a rigid body in space and one single force is acting on it and the force does not pass through the center of mass. I would like to ask why the torque on a body is always the force times perpendicular distance to the center of mass if there is no supporting point on that body? What's the principle behind that?
 A: There is no such principal
We can find the torque about any axis whatsoever we find suitable.
But while facing problems on classical mechanics, there is a singular advantage of finding out the torque through the COM. That is we dont have to account for the torque caused by the body's own weight. 
A: For rigid body in space and one single force is acting on it. If we calculate the moment at different point we obtain different torque. But the body can only have one resultant motion, if different angular acceleration be obtain how do we know which one will be the actual acceleration?
A: There is a principle which states that for a rigid body:


*

*The net loading can be represented as a 3D line, a magnitude and a pitch. This is the loading screw or wrench. 

*The not motion can be represented as a 3D line, a magnitude and a pitch. This is the motion screw or twist.


For both cases the parallel separation of the point of interest from the screw line does not affect the results. This is because a 3D line extends to infinity both ways and due to cylindrical symmetry the resulting vector field is a function of perpendicular distance only.
See https://physics.stackexchange.com/a/80552/392 for the answer to a similar question.
