A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is artificial. For example, when an object may be at rest in our selected frame of reference, yet to an observer is moving at a constant velocity relative to our frame, the same object appears to be in uniform motion with constant velocity. Due to the motion being relative, the object appears to be in static equilibrium to us, while it appears in dynamic equilibrium to the moving observer, and vice versa. Since the laws of physics are identical for all inertial reference frames, there is no distinction between static and dynamic equilibrium in an inertial frame of reference. According to Newton’s second law of motion, the linear acceleration of a rigid body is caused by a net force acting on it. Thus, if a body is in static equilibrium, the sum of all external forces acting on the body must be zero.
This text is adapted from Openstax, University of Physics Volume 1, Section 12.1: Conditions for Static Equilibrium.
