 Free-body diagrams. They are the starting point for almost any engineering analysis, but what are they and why are they so important? The best way to answer this question is to consider an engineering problem. If we look at the lower stage of a rocket shown here, we can deduce that it is likely in static equilibrium, as we do not expect it to be moving in the current scenario. But how could we analyze this? If we think of the forces acting on the rocket, it is clear that the mass of the rocket will exert a gravitational body force, Mg. But I cannot see any other forces acting on the structure in this image. That is because all the other forces are effectively internal forces within the image, and thus consist of equal but opposite action-reaction pairs. In order to isolate the forces acting on the lower stage of the rocket, we need to cut it out of its surroundings, separate the reaction forces the surroundings exert on the rocket from the action forces the rocket exerts on its surroundings. We need to free the body in a way that we can diagram these reaction forces. Before we draw our free-body diagram, let's take a moment to formally define what it is. A free-body diagram is simply a graphical illustration of a structure with all relevant forces and moments acting on it. Calling it a drawing is a bit demeaning to its use in engineering analysis, so I like to think of it as a model, a simplified representation of a structure which can be used to account for the effects of all the loads acting on the structure. Knowing this, let's get back to our rocket example. Here we have our original image of the lower stage of the rocket on the right and the cutout version of the rocket on the left. We notice that we have reoriented the cutout version of our rocket. This will help us make a much more clear free-body diagram as you will see, but it does require some additional information for clarity, a reference coordinate frame. Here we will indicate x as a distance along the rocket and y as the vertical direction oriented towards the ceiling of the hanger, which we cut away in the free-body diagram. Next, we need to start adding the interactions between our rocket and the environment we cut away. We can observe the rocket will have a large mass that would generate a non-negligible body force, its weight, so we can add that to our free-body diagram by including a force at its centre of mass equal to the mass of the rocket m multiplied by the gravitational acceleration g. This, however, cannot be the only force acting on the rocket, otherwise it would accelerate right through the floor of the hanger, which we cut away in our free-body diagram. So we have to look at how the rocket interacts with this. If we take a close look at our rocket, we see that there are two supports at the front and back of the rocket. The front support is on wheels, so it will allow the rocket to slide around the plane of the floor, but prevents it from moving downwards through the floor. In other words, this support constrains the translational degree of freedom of the rocket in the y direction. As we remove the support in our free-body diagram, we need to replace it with a reaction force that can achieve the same result, a force to prevent translation in the y direction. We will label this force Ra in our free-body diagram. If we look at the support at the rear of the rocket, it is not on wheels, but on large flat pads that contact the ground. Unlike the wheeled support, these pads will generate frictional forces that will prevent the pads from sliding on the floor. Thus it will constrain translation of the rocket in the x and y directions in our 2D representation of the body. To represent this in our free-body diagram, we will need to add reaction forces to constrain the motion in the x and y directions. Here I have labeled these reaction forces as RB for the reaction force at B and F for the frictional force preventing sliding of the pads. If you don't completely follow how we obtain the necessary reaction forces to apply at each of the supports, do not worry too much at this point. We will visit this topic in detail in a later video. For right now, just focus on understanding the need to have such forces representing the interaction with the outside world that we cut away when drawing the free-body diagram. The last thing we should add to our free-body diagram to make it complete and ready for use in our engineering analysis is some relevant dimensions. With this diagram, you could now evaluate what reaction forces are necessary to ensure the rocket is in equilibrium. Pretty simple, eh? Well, maybe not at first, but you will get a lot of practice drawing free-body diagrams and you will see that it soon becomes second nature to you. However, this also leads to a common issue I see in engineering analyses, sloppy and incomplete free-body diagrams. To help you avoid this, I want you to remember the memory device known as bread. Let's break down what each of the letters stands for. B stands for body, and it is to remind you that you need to draw the body you are removing from its environment. Now, you don't have to draw the body in as much detail as shown here. A simple outline of that body will suffice. R stands for the reaction forces. This is to remind you to place all of the forces that represent the constraint to the degree of freedom that structures that we cut away, supports that we cut away, exert on that body. E is for the external forces or body forces. In our problem, we had mass times, gravity as a body force, but you might have externally applied loads to deal with as well. A is for the axes. You should always place a coordinate axes. This is important for your equilibrium analysis, establishing directions, but it is just generally really good practice. We need those directions because if we come up with forces as just magnitudes, you only have half the answer because forces are vectors. We need to define directions. Finally, D stands for dimensions. We should put relevant dimensions in our free body diagrams. Now, this last point is a little bit... Some people will disagree with it depending on what other diagrams you have with the structure. A problem might already have the dimensions really laid out quite well, so then you don't necessarily need to replicate it in your free body diagram. But I personally always like to place all relevant dimensions in my free body diagram that I use in my analysis. One last thing before I let you go. There is an important property of free body diagrams that may be obvious to some, but is too important to let slip by without addressing. This has to do with free body diagrams in equilibrium. If we have a free body diagram of a rigid body that has been established to be in equilibrium, that is, the sum of the forces and moments on the body are zero, then the entire body is in equilibrium. As a consequence, any part of that body is also in equilibrium. So, if we cut into our free body diagram as shown here, there must be internal forces and moments within the body that maintain the equilibrium of the part of the body. You will see later in the course that this concept becomes very important when looking at the internal forces acting within a structure.