t = r x F

The magnitude of the torque is given by

    t = r*F*sinq

where q is the smaller of the two angles between the vectors r and F.

For problems in Andes only rotations about a fixed axis in the z direction will be considered.  The result is that torques will only have z components.  Thus

    t_z = + r*F*sinq   for torques that tend to cause CCW rotations and

    t_z = - r*F*sinq   for torques that tend to cause CW rotations.

Note:  The correct sign for the z component of torque can also be obtained by using its general definition.

    t_z = r_x*F_y - r_y*F_x

           = (r*cosqr*F*sinqF) - (r*sinqr*F*cosqF) = r*F*(cosqr*sinqF - sinqr*cosqF)
 
    t_z = r*F*sin(qF-qr)

where qF and qr are the standard orientation angles for F and r with respect to the positive x axis in a CCW direction.