# solving rigid-body equilibrium problems

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There are just two key conditions for rigid-body equilibrium: The vector sum of the forces on the body must be zero, and the sum of the torques about any point must be zero. To keep things simple, we’ll restrict our attention to situations in which we can treat all forces as acting in a single plane, which we’ll call the xy-plane. Then we need consider only the x- and y-components of force in Eq. (11.1), and in Eq. (11.2) we need consider only the z-components of torque (perpendicular to the plane). The first and second conditions for equilibrium are the

The challenge is to apply these simple conditions to specific problems. Problem-Solving Strategy 11.1 is very similar to the suggestions given in Section 5.1 for the equilibrium of a particle. You should compare it with Problem-Solving Strategy 10.1 (Section 10.2) for rotational dynamics problems.

**Caution** :Choosing the reference point for calculating torques In equilibrium problems, the choice of reference point for calculating torques in gtz is completely arbitrary. But once you make your choice, you must use the same point to calculate all the torques on a body. Choose the point so as to simplify the calculations as much as possible.

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