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Torque of a force about the axis of rotation: The turning effect of a force about the axis of rotation is known moment of force or torque due to the force and is measured as the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis of rotation.
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It is given by the Greek letter tou. Thus, torque = force * perpendicular distance from the axis of rotation
Its unit is N m in SI. Its dimensional formula is [M L2 T-2], similar as that of work. It can be pointed out that no doubt, N m is equivalent to joule; but joule is not used as the unit of torque.
Suppose a force 
performing on a particle P. select an origin O and let 
be the position vector of the particle experiencing the force. We describe the torque of the force F about O as ,
... (1)
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This is a vector quantity having its direction perpendicular to and according to the principle of cross product. Now take a rigid object rotating about a given axis of rotation AB (fig b). Let F be a force operating on the particle O of the body. F cannot be in the plane ABP. Take the origin O somewhere on the axis of rotation.
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The torque of F about O is . Its element along OA is known the torque of about OA. To determine it, we could find the vector * and then find out the angle θ it creates with OA. The torque about OA is then 
. Let O1 be any point on the line AB. The torque of F about O1 is
As 
this term will have no element along AB.
Thus, the component of 
is equal to that of
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