Torque Viewed from the Direction k

Missing figure

Viewed from a vantage point far away in the direction k this scene looks like the picture above. We see only the i and j components of the force and the rod. Notice that the vector i or the positive x-axis is pointing to the right and vector j or the positive y-axis is pointing upward. We see the force as the vector (u, v) acting on the end of the rod (a, b). Thus the torque is

(a, b) ^ (u, v) = a v - b u


Copyright c 1997 by Frank Wattenberg, Department of Mathematics, Montana State University, Bozeman, MT 59717