# How would you determine whether an object is at equilibrium? [closed]

How would you determine whether an object is at equilibrium or not?

What is the definition of equilibrium?

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By comparing the object against the definition of equilibrium of course. Could you be more specific about what you're having trouble understanding? –  David H May 1 at 0:50
This question (v3) seems closable since a straightforward Google search would immediately provide the answer, cf. e.g. this and this meta post. –  Qmechanic May 31 at 7:55
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## closed as too localized by ja72, Waffle's Crazy Peanut, Brandon Enright, Emilio Pisanty, twistor59Jun 7 at 16:13

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## 3 Answers

Static equilibrium requires that the sum of all forces is 0,$$\sum F=0$$ and the sum of all torques is 0, $$\sum \tau =0$$ Be aware that force and torque is a vector; they have both magnitude and direction.

You will usually want to separate a force into its components such that all forces are either parallel or perpendicular to each other. Then apply the equation above for force separately for x- and y- axes.

The direction of torque follows the right-hand rule. If unsure, just think of counter-clockwise as positive and clockwise as negative. Then apply the equation for torque.

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There a several notions of equilibrium. These are discussed in an informative online encyclopedia called "Wikipedia", which I recommend. The link to the mechanical equilibrium section is here. (I assume you mean mechanical equilbrium since there is the forces tag.) If you read the article and have trouble understanding anything, please ask a more specific question about what you are having trouble understanding.

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I'll do my best to answer this with the information provided.

In the most general (and hand-wavy) sense possible, something has reached equilibrium if after a while it has stopped changing in some way. For example, if you put a warm person in a cold room the person will warm the room up ever so slightly and the room will cool the person down. Whilst the temperatures of the room and the person are changing there is no equilibrium. But after a while of being in the room the person will cool down more slowly and, conversely, the room will warm up more slowly. Given enough time the persons temperature will stop changing all together (the person's temperature would be less than when they first walked in but it will have stopped dropping given enough time). Likewise the room will stop warming up (assuming there is some refrigeration working that was cooling it down in the first place). This should be easy to imagine. When you walk outside on a cold day, you cool down but you don't just carry on getting colder for ever until you eventually freeze over (unless of course your metabolism slows down in which case you're probably dying)(although even then, you'd eventually reach the same temperature as the surrounding air and then your temperature would stop changing). When the temperature of the room has stopped changing and the temperature of the person has stopped changing (which will happen at the same time) we say the two 'systems' (the room and the person) have reached equilibrium.

I noticed you tagged 'forces' so I'm guessing you want to know about equilibrium with regards to forces on objects. Although the above stuff about temperature is also very important to know!

Equilibrium with forces basically means that all the forces on an object cancel, so that overall there is no 'net' force on the object. For example if you're hanging from a rope by your hands, the tensile force of the rope pulling you up is of equal size but of opposite direction to the force of gravity pulling you down. As a result you don't accelerate either upwards or downwards, you just stay there until you're too tired and hungry and probably need the loo. Similarly if you're moving forward on an ice rink on skates (assume no friction so you carry on at the same speed for ever) and someone pushes you to the right exactly at the same time as someone pushes you to the left with exactly equal force then you'd just carry on gliding forward as though nothing happened. You've still got velocity but the velocity hasn't changed. Or in other words because the forces on you completely cancelled your acceleration remained at zero. So I guess you could say that, when talking about forces, equilibrium means no change in velocity which is the same as saying zero acceleration at all times. It is important to remember though: You can still have non-zero velocity and experience an equilibrium of forces. The ice skater in our example was moving the whole time and had non-zero velocity, but the velocity didn't change which is the exact same thing as saying acceleration was zero.

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