What Are the Torques on a Rectangular Plate in Equilibrium?

[zezima1]

Consider the system on the attached picture showing a rectangular plate attached to a pole by two screws - one in A and one in B. Now to figure out the condition for equilibrium one would calculate the torques around point A and B to find that one screw must be pulling and the other one pushing the plate with a horizontale force of equal magnitude.

Now my problem is that I have never really understood this whole idea, that you should be able to get zero torque around every possible rotation axis. Does that then mean that you can also calculate the torque around for instance a point C halfway up the rod?
If so let's try do that. I marked C on the picture. Then you get a torque equal to ½bmg. But wouldn't that then mean that the force in point A is creating an extra torque as seen from a point of view where C is that axis of rotation?

 

[Doc Al]

Now my problem is that I have never really understood this whole idea, that you should be able to get zero torque around every possible rotation axis. Does that then mean that you can also calculate the torque around for instance a point C halfway up the rod?

Sure. You can use any point for calculating torques. (Some may prove easier than others.)

If so let's try do that. I marked C on the picture. Then you get a torque equal to ½bmg.

That's the torque about C due to the weight of the plate. Now include the torques due to the forces at A and B.

But wouldn't that then mean that the force in point A is creating an extra torque as seen from a point of view where C is that axis of rotation?

Not sure what you mean. You'll get the same values for the forces at A and B as you would have using any other point as your axis.

 

[zezima1]

Hmm I got it now, I wasn't thinking properly. Thanks