5.5: Static Equilibrium
Pivots and Torque Reference Points
The definition of torque ( Equation 5.4.6 ) includes the position vector \(\overrightarrow r\), which points from a reference point to the point where the force is applied. When we are interested in how the torque is accelerating the object rotationally around a fixed point ("pivot"), it is convenient to choose the reference point to be that fixed point. This is because the forces applied at that fixed point (to keep it fixed) provide zero torque when referenced there, and those forces are generally not known. We explore here the effect of changing the reference point in the particular case when there is no net force , though perhaps there could be a net torque. The net torque around a given reference point is:
\[ \overrightarrow \tau_{net} = \overrightarrow r_1 \times \overrightarrow F_1 + \overrightarrow r_2 \times \overrightarrow F_2 + \dots \]
The reference point is located at the tails of the \(\overrightarrow r_i\) vectors, but suppose we want to change that reference point. We can do this by simply adding the same constant vector \(\overrightarrow r_o\) to every position vector. This has the effect of shifting the reference point from the point of \(\overrightarrow r_o\) to its tail, as shown in the figure below [ Note: The figure shows only two of the many forces applied. ]