Free-Body Diagrams and Equilibrium: Of Special Interest to Physics C Students

Practice problems for these concepts can be found at:

Free-Body Diagrams and Equilibrium Practice Problems for AP Physics B & C

It must be emphasized that even Physics C students must go through the four-step problem-solving process. Frequently, Physics C students try to take shortcuts, thinking that equilibrium problems are easy, only to miss something important. If free-body diagrams are good enough for professional physicists to use, they are good enough for you.

The Physics C exam will often expect you to find the torque provided by a force that acts at an angle. For example, consider a force F acting on a bar at an angle θ, applied a distance x from a pivot. How much torque does this force provide ? See Figure 10.7.

To solve, break the force vector into horizontal and vertical components, as shown in Figure 10.8.

The vertical component of F applies a torque of (F sinθ)x. The horizontal component of F does not apply any torque, because it could not cause the bar to rotate. So, the total torque provided by F is (F sinθ)x.

Lever Arm

The "lever arm" for a force is the closest distance from the fulcrum to the line of that force. Then, the torque provided by a force is the force times the lever arm.

Consider Figure 10.9, which represents the same situation as does Figure 10.7. Instead of breaking F into components, continue the line of the force. The torque is F times the lever arm shown in the diagram. By trigonometry, you can see that the lever arm is equal to x sinθ. No matter how you look at it, the torque provided by F is still (F sinθ)x.

Practice problems for these concepts can be found at:

Free-Body Diagrams and Equilibrium Practice Problems for AP Physics