12.5: Rigid Body Equilibrium Problems – I

A rigid body is said to be in static equilibrium when the net force and the net torque acting on the system is equal to zero. To solve for rigid body equilibrium problems, do the following steps.

• Step 1: Identify the object to be analyzed and all forces acting on the object. In addition, identify the known and unknown variables in the given problem.
• Step 2: Set up a free-body diagram for the object. Choose the xy-reference frame for the problem. Draw a free-body diagram of the object, including only the forces that act on it. Label all forces in the x- and y-directions. For an unknown force, the direction must be assigned arbitrarily, that is, as a working direction. A plus sign (+) means that the working direction is the actual direction. A minus sign (−) means that the actual direction is opposite to the assumed working direction. Also, choose the location of the pivot point with respect to which all the forces are computed.
• Step 3. Set up the equations of equilibrium for the object. Use the free-body diagram to write a correct equilibrium condition for the force and torque components in the x-y direction and along the axis of rotation, respectively
• Step 4. Simplify and solve the system of equations for equilibrium to obtain unknown quantities. The number of equations should be the same as the number of unknowns. Then, evaluate the expressions for the unknown quantities.

This text is adapted from Openstax, University Physics Volume 1, Section 12.2: Examples of Static Equilibrium.