Translational Equilibrium: What It Is and How to Find It

translational equilibriumClueless about physics? Not to worry – we’re here to fill you in on the what and how behind translational equilibrium, complete with definitions, examples, and formulas. Whether it’s to pass your science class or just fill a pesky knowledge void, this article is here to help.

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What Is Equilibrium?

Equilibrium is achieved when the total net force on an object has a sum of zero. Something that’s in equilibrium doesn’t speed up or slow down – it either maintains a constant velocity or remains motionless.

Newton’s first law is extremely relevant to translational equilibrium. It says that “every object persists in its state of rest or uniform motion­ in a straight line unless it is compelled to change that state by forces impressed on it”. In layman’s terms, things stay still or continue moving at the same speed – unless acted upon by something else, whether that be gravity, your foot, or the pressed brake on your car.

It’s also known as the law of inertia. The law of inertia relates to equilibrium because they are essentially one and the same. When an object’s at rest or moving at a constant velocity, as described in the first law, it’s in equilibrium – until some random force comes along and throws everything out of whack.

Translational vs Rotational

So where does the translational part come in? There are two main types of equilibrium and they are called translational equilibrium and rotational equilibrium. Translational equilibrium relates to any forces on any object. If all the forces acting on a particular object add up to zero and have no resultant force, then it’s in translational equilibrium.

Examples would be an acorn falling from its tree at terminal velocity, a book resting on a bookshelf, or someone walking at a steady, constant speed. On the other hand, if the acorn has just broken from it’s branch and is still accelerating towards terminal velocity, this would not be considered translational equilibrium. Neither would a book being pulled from the shelf to be read or a person slowing to a stop after a brisk jog through the park.

Want to guess what rotational equilibrium applies to? That’s right, an object’s rotation or torque, also known as angular velocity. An object that’s not rotating or doing so at a steady speed, the sum of the torques acting on it equaling zero, is at rotational equilibrium.

Some examples of this are a Ferris wheel turning at a constant velocity, two children of equal weight balanced on either side of a seesaw, or the Earth rotating on its axis at a steady speed. Now, put a child on one end of the seesaw and an adult on the other and you no longer have rotational equilibrium. Same thing with a Ferris wheel slowing down to end the ride and drop off its passengers. But let’s hope the Earth never slows down or speeds up enough to lose rotational equilibrium, for all our sakes.

An object can be in both translation and rotational equilibrium, neither, or just one or the other. The book sitting on a shelf, for instance, would fit both requirements since it’s not moving at all. It will, however, be tough to find an object that is both rotating and moving in a straight line at a constant velocity since there simply aren’t many times when that situation occurs in everyday life.

Dynamic vs Static

We say an object is in dynamic equilibrium when it’s in motion. An example of this would be a car traveling at a constant speed of 45 mph. Because it’s not accelerating or decelerating, it is still considered in equilibrium, but it’s movement makes it dynamic.

Static equilibrium is the opposite. Your pen on the desk beside you would be a good example of this form of equilibrium. It is not moving, therefore it’s obviously not accelerating or decelerating either and is therefore in static equilibrium.

How to Determine Translational Equilibrium

Now that we know and understand what translational equilibrium actually is, it’s time to learn how to figure out when something is in equilibrium without simply looking at it – or when that’s not an option. You can do this with word problems or anything else you’re curious about. This will require a little math, but don’t worry – Udemy’s got you covered. But we’ll get to that when the time comes.

  • Draw Your Diagrams

First things first, read or analyze your problem and visualize the situation in your head. You’re going to want to then sketch out the situation on a piece of paper. For a word problem, you may want to use a free-body diagram.

A free-body diagram is essentially a picture of the objects in question. It doesn’t have to be a piece of art, just a rough sketch to make it easy to get your bearings and see what goes where. Once you’ve found the object the forces are all acting upon, you can label your x, y, and z components to create a force diagram. This will look less like a picture and more like a graph or triangle.

  • Find and Add the Forces

Now you can go ahead and label any forces and angles that you can find. But before you get carried away, let’s talk about the difference between action forces and reaction forces. Action forces are what the other objects – whether they be a wall, a weight, or simply gravity – are exerting on the object you’re trying to solve equilibrium for. This is a positive force.

Reaction forces are, well, reactive. They’re the opposite and deal with the force of the object in question acting on everything else. They’re negative forces.

Any force value you don’t already know can be found with a little geometry and trigonometry. Fortunately, if you’re a little rusty in those areas, you can find a great course on geometry here and another really excellent course for trigonometry in this link.

Then you’ll apply the First Condition of Equilibrium. It states that the sum of all of the forces acting upon the object must equal zero, meaning there’s no resultant force. So add all of your forces and up and find their sum. If they all cancel each other out, congratulations! You have an object in equilibrium.

Apply What You’ve Learned

You might not quite be an expert on translational equilibrium just yet, but with a little more practice and studying you’ll have it in no time. Meanwhile, try spotting the things in equilibrium during your daily life – in your classroom, bedroom, or on the street. Is it translational or rotational equilibrium? Dynamic or static?
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