Torque as a vector quantity

• The vector or cross product is another way to combine two vectors; it creates a vector perpendicular to both it the originals.
• In vector form, torque is the cross product of the radius vector (from axis of rotation to point of application of force) and the force vector.

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There are other ways of computing and expressing the cross product of two vectors. For example, given two vectors A and B in the standard unit-vector notation

one can combine the components of the two vectors to form the cross product A x B like so:

One way to remember this particular arrangement is to consider the cross product as a determinant (see Appendix E of your physics text):

We are interested in one particular cross product:

Note several things:

• the maximum size of the torque is the product of the magnitude of r and the magnitude of F
• the direction of the torque will be perpendicular to both r and F
• if a force points straight toward (or away from) the axis of rotation, then the torque due to that force is zero