It’s the same state of two interacting parts of a system. Think of an inflated balloon in a normal room: the air inside the balloon is at a higher pressure than the air outside. If you open it up, the air rushes out until the pressure difference is eliminated. At that point, the pressures are at equilibrium.
Similarly with a fresh cup of coffee. It’s hotter than its environment. Heat would continue to be transferred from the cup to the air and surrounding surfaces at a decreasing rate as the temperature difference is reduced, until they are the same. That would be an example of temperature equilibrium, when the transfer considerably stops.
For a movement example, a skydiver. Gravity accelerates them downwards. As they gain speed, air resistance (an upward force in this case) increases. Once the air resistance and gravity become equal, the person stops accelerating and falls at a steady rate. The forces are said to be in equilibrium because the change in velocity has gone to zero.
Physicists are often interested in how forces interact. Force A is pushing a certain amount one way, while Force B pushes a certain amount the other, etc. An equilibrium is a setting where all these forces counteract each other and nothing happens.
You are probably in an equilibrium now. Gravity is pulling you towards the Earth, but whatever surface you are resting on is pushing back equally hard, so you stay put. The idea of terminal velocity comes from an equilibrium in acceleration. As an object falls, it accelerates, but this increases the wind resistance. An equilibrium is achieved when the acceleration due to gravity is perfectly cancelled out by the change in wind resistance. The object is still falling, but its speed is no longer changing.
Let’s say I have a rock tried to a string. If I hold up the string letting the rock dangle, it’s in equilibrium. The rock is being pulled down by gravity as hard as it’s being pulled up by the string, resulting in a rock that doesn’t accelerate. If I push the rock to one side, it will swing back and forth through that equilibrium point because the string is pulling it sideways whenever it is not pointing straight up and down. As a result, the forces don’t cancel out, causing acceleration. Eventually friction will slow the rock down and it will stop in that equilibrium point. This is a stable equilibrium.
An unstable equilibrium would be like balancing a pencil upright on your finger. When the pencil is perfectly upright, it will stand, but the slightest jostle will make it fall over. It’s in equilibrium, but there’s no restoring force to bring it back there.
It can be more than forces too. Anything that tries to change a system can be canceled out by something trying to.cause the opposite of that change.
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