Torque: Difference between revisions
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When applying a force to an object at an angle <math>{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>{\vec{F}}</math> relative to a location (A). | When applying a force to an object at an angle <math>{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>{\vec{F}}</math> relative to a location (A). | ||
<div style="text-align: center;">[[File:torquemag_formula.png |150x40px]]</div> | |||
For a purely perpendicular force with a force application at <math>{θ}=90{°}</math>, <math>sin{θ}=1</math> and the torque is r<sub>A</sub>F. For a force that is parallel to the lever arm at an angle <math>{θ}=0{°}</math>, <math>sin{θ}=0</math> and the torque is zero. | For a purely perpendicular force with a force application at <math>{θ}=90{°}</math>, <math>sin{θ}=1</math> and the torque is r<sub>A</sub>F. For a force that is parallel to the lever arm at an angle <math>{θ}=0{°}</math>, <math>sin{θ}=0</math> and the torque is zero. | ||
Revision as of 08:36, 5 December 2015
The Main Idea
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.
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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History
The concept of torque originated
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