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Torque

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.

The Main Idea

In "Matter & Interactions, Fourth Edition," torque is defined as τ = r_A x F . Applying a torque to an object changes the angular momentum of that object. Torque, in angular momentum calculations, is analogus to F_net in regular momentum calculations. Just like how a collection of forces acting on a system is called F_net, a collection of torques acting on a system is τ_net.

A Mathematical Model

Torque is defined as the cross product of the distance vector, the distance from pivot point to the location of the applied force, with an applied force. The magnitude of torque can be defined as such:

• τ_A = r_AFsinθ

To determine the direction of torque, one can either compute the cross product or apply the "right-hand rule." To use the "right-hand rule," point your fingers in the direction of r_A and curl your fingers in the direction of F.

If your thumb points up, the force is coming out of the page and is in the positive z-directon. If your thumb points down, the force is going into the page and is in the negative z-direction.

A Computational Model

Examples

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