However, the second condition involves torque, which is defined as a cross product, τ → k = r → k × F → k, τ → k = r → k × F → k, where the position vector r → k r → k with respect to the axis of rotation of the point where the force is applied enters the equation. The first condition involves only forces and is therefore independent of the origin of the reference frame. The first and second equilibrium conditions are stated in a particular reference frame. The second equilibrium condition means that in equilibrium, there is no net external torque to cause rotation about any axis. Since the laws of physics are identical for all inertial reference frames, in an inertial frame of reference, there is no distinction between static equilibrium and equilibrium.Īccording to Newton’s second law of motion, the linear acceleration of a rigid body is caused by a net force acting on it, or Because the motion is relative, what is in static equilibrium to us is in dynamic equilibrium to the moving observer, and vice versa. Notice that the distinction between the state of rest and a state of uniform motion is artificial-that is, an object may be at rest in our selected frame of reference, yet to an observer moving at constant velocity relative to our frame, the same object appears to be in uniform motion with constant velocity. We say that a rigid body is in static equilibrium when it is at rest in our selected frame of reference. This means that a body in equilibrium can be moving, but if so, its linear and angular velocities must be constant. We say that a rigid body is in equilibrium when both its linear and angular acceleration are zero relative to an inertial frame of reference. Explain how the conditions for equilibrium allow us to solve statics problems.Draw a free-body diagram for a rigid body acted on by forces.

Identify the physical conditions of static equilibrium.By the end of this section, you will be able to:

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