# What Is the Condition for the Static Equilibrium of a Rigid Body?

For a rigid body to be in static equilibrium, without total acceleration, two conditions must be met. First, the vector sum of all forces acting on it must be zero (translational equilibrium). Second, the sum off all torques due to any external force on any axis must be zero (rotational equilibrium).

The exact meaning of a body being in equilibrium is that there is no total acceleration, regardless of whether or not there is a velocity. By Newton's laws of motion, for acceleration to occur, an object must be acted upon by an unbalanced force or an unbalanced torque. For a rigid body, two types of motion is possible: rotational and translational. If the vector sum of all forces acting on the rigid body is equal to zero, then there is no unbalanced force and therefore no translational acceleration, thus the rigid body is in translational equilibrium. If the sum of all torques acting on the rigid body is zero, then there is no unbalanced torque and therefore no rotational acceleration, meaning the rigid body is in rotational equilibrium. When a rigid body has both translational equilibrium and rotational equilibrium, there is no total acceleration and static equilibrium is attained.

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