Torque Using Cross Product

Consider the torque (turning force) on a wrench that is tightening or loosening a bolt. If a force of newtons (N) is applied to the end of a wrench of length meters (m), the torque is given by the cross product . Its magnitude is then N m, where is the angle between the vectors and .
This Demonstration illustrates the spatial arrangement of the vectors , and for selected values of , and for either tightening or loosening the bolt. Use the "turn" control to see how torque varies.


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[1] J. Stewart, D. K. Clegg and S. Watson, Calculus: Early Transcendentals, 9th ed., Boston: Cengage Learning, 2021 p. 861.
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