Torque
Torque is the measure of who much a force acting on an object causes that object to rotate, creating a tendency for the object to rotate about an axis, fulcrum or pivot. Torque is most commonly classified as "twist", rotational force, or angular force to an object and applying it to a system changes the angular momentum of the system. The effectiveness of torque depends on where the force is applied and the position at which the force acts relative to a location.
History
The concept of torque first originated with Archimedes studies focused on levers. While he did not invent the lever, his research and work on them caused him to create the bock-and-tackle pulley systems, allowing people to use the principle of leverage to lift heavy objects. Building off of this, he explained how torque comes into play with objects that are twisting or rotating around a pivot, just as a lever does around the point of rotation. Using the Law of the Lever and geometric reasoning, Archimedes developed the concept of torque.
In 1884, the term "torque" was introduced into English scientific literature by James Thomson, a notable scientist remembered for his work on the improvement of water wheels, water pumps, and turbines.
A Mathematical Model
Torque is the cross product between the distance vector, a vector from the point of pivot (A) to the point where the force is applied, and the force vector. The force vector, [math]\displaystyle{ {\vec{F}} }[/math], is defined about a particular location.
When applying a force to an object at an angle [math]\displaystyle{ {θ} }[/math] to the radius, a different equation is required to capture both the force of the twist and the distance from the pivot point to the place where the force is applied. This equation finds the magnitude of torque exerted by a force, [math]\displaystyle{ {\vec{F}} }[/math] relative to a location (A).
For a purely perpendicular force with a force application at [math]\displaystyle{ {θ}=90{°} }[/math], [math]\displaystyle{ sin{θ}=1 }[/math] and the torque is rAF. For a force that is parallel to the lever arm at an angle [math]\displaystyle{ {θ}=0{°} }[/math], [math]\displaystyle{ sin{θ}=0 }[/math] and the torque is zero.
A Computational Model
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