[Answer] What does it mean to say something is in mechanical equilibrium?

Answer: An object in mechanical equilibrium experiences a zero net force.
What does it mean to say something is in mechanical equilibrium?

In classical mechanics a particle is in mechanical equilibrium if the net force on that particle is zero. By extension a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent…

In classical mechanics a particle is in mechanical equilibrium if the net force on that particle is zero. By extension a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity that particle is in static equilibrium. Since all particles in equilibrium have constant velocity it is always possible to find an inertial reference frame in which the particle is stationary with respect to the frame.

An important property of systems at mechanical equilibrium is their stability . Potential energy stability test If we have a function which describes the system’s potential energy we can determine the system’s equilibria using calculus. A system is in mechanical equilibrium at the critical points

An important property of systems at mechanical equilibrium is their stability . Potential energy stability test If we have a function which describes the system’s potential energy we can determine the system’s equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system’s potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable we apply the second derivative test . With ${\displaystyle V}$ denoting the static equation of motion of a system with a single degree of freedom we can perform the following calculations: Second derivative < 0 The potential energy is at a local maximum which means that the system is in an unstable equilibrium state. If the system is displaced an arbitrarily small distance from the equilibrium state the forces of the system cause it to move even farther away.: ${\displaystyle {\frac {\partial ^{2}V}{\partial q^{2}}}>0}$ Second derivative > 0 The potential energy is at a local minimum. This is a stable equilibrium. The response to a small perturbation is forces that tend to restore the equilibrium. If more than one stable equilibrium state is possible for a system any equilibria whose potential energy is higher than the absolute minimum represent metastable states.: ${\displaystyle {\frac {\part…

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