## Introduction

In this post, we will learn how to solve static equilibrium physics problems with translational and rotational equilibrium equations.

Check out our Patreon page for FREE and low-cost physics practice problems with solutions.

### What is Static Equilibrium?

Static equilibrium means that the forces and torques on an object are balanced, so the object does not have acceleration.

No acceleration means that our object could be at rest OR moving at a constant velocity.

### What is Translational Equilibirum?

Translational equilibrium means that the sum of the forces is equal to zero.

We can only add forces that have the same direction, so this means we will have three equations:

- The sum of forces in the x-direction is equal to zero
- The sum of forces in the y-direction is equal to zero
- The sum of forces in the z-direction is equal to zero

### What is Rotational Equilibrium?

Rotational equilibrium means that the sum of the torques is equal to zero.

In some courses, they use the term “Moments” instead of “Torques”.

The sum of torques equal to zero means that we have no angular acceleration: We are either not rotating or we are rotating at a constant angular velocity.

We can only add torques that have the same direction, so this means we will have three equations:

- The sum of torques in the x-direction is equal to zero
- The sum of torques in the y-direction is equal to zero
- The sum of torques in the z-direction is equal to zero

## Solving Static Equilibrium Problems in 4 Steps With An Example

Let’s look at an example to see how to solve static equilibrium problems with both translational and rotational equilibrium.

### 1. Read the Problem and Form a Strategy

The first thing I do is read the problem and look for what information they gave us and what they are asking for.

In static equilibrium problems, they usually give a diagram of the system with dimensions and the mass of an object, then ask you to solve for a force, like tension.

### 2. Draw a Free-Body Diagram (FBD)

Now that we know what they are asking for, we need to draw a free-body diagram.

For our problem, we will draw an FBD of the beam by drawing a line.

For beams, we should mark down how our beam is connected to the wall.

This could be a pin joint, a roller joint, or a fixed connection like a weld.

For us, this is a pin joint, which means there could be forces in both the x and y directions, but no torques.

Now that we have our mass represented on the FBD, we will write down and label all of the forces acting on the object.

### 3. Write Out Your Equilibrium Equations

Now that we have an FBD we need to decide which equilibrium equation we want to use first.

Let’s start by writing out our three equilibrium equations, and then see which one is easiest to solve.

#### The Sum of Forces in the X-Direction Equal to Zero

For the x-direction forces that point to the right will be positive and forces that point to the left will be negative.

Since the tension is on an angle, we need to use only the x-component of that force in our equation.

### The Sum of Forces in the Y-Direction Equal to Zero

For the y-direction forces that point up will be positive and forces that point down will be negative.

Since the tension is on an angle, we need to use only the y-component of that force in our equation.

### The sum of Torques Equal to Zero

For the torques, we have set counter-clockwise rotation to be positive and clockwise rotation to be negative.

Since the tension is on an angle, we need to use only the perpendicular component of that force in our equation.

### 4. Solve For Your Unknowns

First, solve for the Tension Force from the rotational equilibrium equation.

Next, solve for the Reaction Force at the pin in the x direction from the sum of forces in the x direction equation.

Lastly, solve for the Reaction Force at the pin in the y direction from the sum of forces in the y direction equation.

## Check Out These YouTube Videos to See Solved Examples

When I was in engineering school, I always started studying by watching YouTube videos (shoutout The Organic Chemistry Tutor).

Seeing other people solve problems helped me understand the thought process behind the steps to the solution.

Once I got the basics, I would start solving practice problems myself.

I am working on a Physics video series on YouTube where I go through theory and practice problems.

Check out these videos below!

### Translational Equilibrium Videos

### Rotational Equilibirium Videos

## Where Do I Find Static Equilibrium Practice Problems?

Once you have watched a couple of YouTube videos, it’s time to practice for yourself!

Check out our Patreon page for FREE and low-cost physics practice problems with solutions.

## Where Do I Get Extra Help With My Physics?

Want answers to more specific equations?

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