In AP Physics, one of the more common torque problems you will be asked to solve are Beam or Brigde Problems. This type of problem is an expansion of the concept of Rotational Equilibrium, so you should read my page on Equilibrium and Torques and have a good understanding of that concept before trying any of the problems here.
First of all, remember that objects in equilibrium have a net force in both the X and the Y direction of zero. Objects that have the potential to rotate that are in equilibrium also have a net torque of zero. A beam or a bridge is an example of an object in equilibrium and as it is rigid, it has a potential to rotate. Thus both of the equilibrium statments can be applied to their case and used to find missing values and the like.
Take the following picture as an example:
Here we have a drawing of a simple bridge drawn with arrows to show all the forces acting on it. Column A and B each exert an upward force on the plank or beam that runs across them to form the bridge. The plank also exerts a downward force thanks to its weight (mg). Since the brigde is neither accelerating in an upward or downward direction, we know that it is in equilibrium. This means that the sum of all the forces acting upward (A & B) totalled with the sum of all downward forces (its weight) is equal to zero.
Next we should examine the torques acting on the bridge.
We pick a place for the pivot point to be. In reality, where you decide to place the pivot point isn't important. A rigid object can rotate at any point, so therefore it makes sense that any place you pick will work. You need to consider it for looking at torques, so you must pick a location. When considering where to place a pivot point, usually just go with what is the most convenient. I placed mine right in the center where the weight is, so that since the weight is no distance from the piviot point, it generates no torque, so I only have to concern myself with the two forces on the ends. Choosing your pivot point so that one of the forces no longer needs to be considered when calculating torques, is a good way to save yourself some work.
Now let's look at how you's calculate the torque values:
Looking at the picture, we can see how each of the forces will act against each other in terms of rotation. If the pivot point is in the center Force B will generate a counterclockwise torque while Force A will generate a clockwise torque. If this is not evident to you, follow the lines I have drawn showing each's rotation. Since this is true the torque generated by A and that generated by B must add to zero.
To calculate torque A one must multiple Force A by the l value as that is the perpendicular distance from the pivot point or the lever arm. The same goes for torque B. A problem on a test would have number values given for you to calculate an unknown, but this example is simply to illustrate a few key points for working through the problem. To see the kind of problems you would get, follow the links to the solved sample problems and the problems for you to try at the bottom of this page.
Problems For You To Try