We already know that for an object to be in equilibrium, there must be no net acceleration. This is the definition of Equilibrium, as we learned when we discussed forces and Newton's Laws in earlier chapters in the AP Program. Zero acceleration also translates to zero net force or that the sum of all the forces acting on the object is zero.
You read in the Introduction to Torques section that a torque is equal to Force multiplied by the lever arm. Since when an object is in equilibrium has a net force of zero, it makes sense from the torque formula that the net torque should also be zero.
When examining real-life situations, this make sense as when we think of an object in equilibrium we think of forces being "balanced" or that sum of the forces on both the X-Axis and the Y-Axis adds to zero. This is true for all types of matter. However with rigid bodies we know that forces don't just cause acceleration on the X and Y-Axis. Forces can cause rotation as they result in torques. An object in equilibrium is in a sense "balanced" and thus does not rotate as the net force is zero. This brings us to the statement of the conditions for a rigid body to be in equilibrium.
This statement is true for any rigid body that is in equilibrium, and can be used to find values in many problems where we have an object in rotational equilibrium.
It is also important to understand that a net torque of zero means that the sum of the torques acting in the clockwise and counterclockwise directions equals zero. A torque of +36 N*m (or 36 N*m counterclockwise) and a torque of -36 N*m (or 36 N*m in a clockwise direction) yields a net torque of zero. This law of torques, that states that for an object to be in rotational equilibrium, the sum of all clockwise and counterclockwise torques must be zero is known as the Principle of Moments.
In AP Physics the most common rotational equilibrium problems you will encounter are bridge or beam problems and ladder problems. Since these two are very important to understand, I have created two separate sections to explain each one in greater detail. Now that you understand the basic concepts of Rotational Equilibrium, you should head to these sections to analyse each individual case as they can vary slightly depending on piviot point locations and angles. Each of these sections will contain the sample and practice problems pertaining to equilibrium and torques.
