12.1:
Static Equilibrium – I
Equilibrium is the condition when the motion of a body does not change with time. It can be categorized as static or dynamic equilibrium.
In static equilibrium, the object is at rest. Whereas, if it is moving with constant velocity, the object is said to be in dynamic equilibrium.
For a system to be in static equilibrium, it should satisfy two conditions simultaneously. First, its translational velocity should be zero, for which there should be no net external force acting on the body. Second, its rotational velocity must be zero. This is satisfied when net torque due to all the external forces acting on it is zero.
Consider a freely-moving weighing balance having equal masses on each side. A static equilibrium is established when the net force and the net torque acting on the system are balanced.
12.1:
Static Equilibrium – I
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.