How to find net torque?

Question

For the meter stick in Figure 10-4, what is the magnitude of the net torque due to both forces $F_1$ and $F_2$ about an axis perpendicular to the page through point $A$? Is it clockwise or counterclockwise? Show your work.

How do I do this? Book doesn't explain anything.

Do I just subtract $B$'s torque from $A$? $105 - 1 = 104$?

Answer 1

Torque is the wedge product of the radial vector from the axis of rotation to the point at which the force is applied and the force vector. I.e. $${\bf\unicode[STIXGeneral]{x03c4}} = \mathbf r \wedge \mathbf F$$

The net torque will be the sum of all the torques added (bi)vectorially.

In this case you have $${\bf\unicode[STIXGeneral]{x03c4}} = (0.1\,\mathbf{\hat x}\textrm{ m})\wedge (-10\,\mathbf{\hat y}\textrm{ N}) + (0.7\,\mathbf{\hat x}\textrm{ m})\wedge (-15\,\mathbf{\hat y}\textrm{ N}) = -11.5\,\mathbf{\hat x}\wedge\mathbf{\hat y}\textrm{ Nm}$$

So the magnitude of the torque is

11.5 Nm

and the direction is

clockwise.