Part 1: Clarifying terms

Orthodontics is probably the specialty that most depends on basic concepts and principles of physics. However, many of these principles are ignored or misunderstood by those who consistently practice the same fundamental act in their clinical routine: applying FORCES to move teeth.

We cover in this post the famous laws of Newton. They are: 1) LAW OF INERTIA: every object continues in its state of rest or uniform motion in a straight line, unless an external force (read unbalanced *) acts on it; 2) ACCELERATION: the acceleration or change of movement is proportional to the applied force; and 3) ACTION AND REACTION: for every force of action, there is an equal and opposite force.

The good news is that only ONE law requires a detailed explanation in order to be appropriatelly understood. This is the law of inertia, the most important for our clinical practice. More specifically, we need to understand this state of rest that  an object keeps when it is not subjected to an unbalanced force *. I used this term because it is perfectly possible for an object to be in this state of rest, called STATIC EQUILIBRIUM, even suffering the action of forces. For this purpose, we only need that the forces are being counteracted by each other. An orthodontic spring compressed by equal and opposite forces (eg. placed between two teeth) represents a classic example of this equilibrium condition (Figure 1). The spring changed its shape due to elastic deformation, but it is not accelerating neither to the right nor to the left. It remains at rest. It’s hard to imagine how an appliance at rest can exert forces to move teeth, but the fact is that ALL appliances attached between teeth will be at rest – in static equilibrium, similarly to the spring of our example.


FIGURE 1. A. deactivated open spring. B. When applying two equal and opposite forces on the spring, the spring will change its shape by elastic deformation, but it will not accelerate. Note the lack of movement in relation to a fixed reference point (x). The spring is in EQUILIBRIUM on both situations – A and B.

So, what is the cause of the forces responsible for tooth movement?

It is time to talk about the Newton’s third law, commonly and incorrectly addressed  in some orthodontic books. In fact, its application in orthodontics is quite SIMPLE, as explained in the following paragraphs:

Consider the previous example of the open spring inserted between two teeth (Figure 2). Now, we know that the spring must be in equilibrium, so it is easy to observe the activation forces, described as the forces needed to activate (or install) an appliance. Note that the brackets exert this ACTION forces on the spring, and the spring, in turn, react with equal and opposing forces, which are the REACTION forces exerted on the brackets. The forces perceived by the teeth are called deactivation forces, and they are the ones that interest the professional, because they will be the main determinants of the direction of tooth movement.


FIGURE 2. The compressive forces needed to maintain the spring in equilibrium between two teeth are called activation forces (blue arrows). In this figure, the brackets are replacing the fingers of the previous figure. The 3rd Newton’s law is expressed by the interaction between the blue and red arrows. The brackets keep the spring compressed and the spring reacts with the deactivation forces (red arrows), which will act as the spring is returning to its original shape. These reactive forces are the ones that will move the teeth.

The determination of the deactivation forces is an extremely simple process and does not require any formula or mathematical calculation. If we know the activation forces, we simply revert the sense of the activation forces in order to obtain the deactivation forces. This is the law of action and reaction. It can be easily verified in the preceding example and in the following figure (Figure 3), now using an elastic to generate the force. Please see the figure to clarify any doubt or confusion regarding the principle of equilibrium and the law of action and reaction.


FIGURE 3. A) An orthodontist exerts a force of 60g for bringing an elastic from the molar to the canine. B) Once the elastic is engaged, it remains stretched and keeps its state of equilibrium, suffering two equal and opposite actions – blue arrows: the activation forces. This principle is EQUILIBRIUM. On the other hand, the 3rd Newton’s law is expressed by the interaction between the blue and red arrows. The brackets keep the elastic stretched, and the elastic reacts with the deactivation forces (red arrows), which will act as the device is returning to its original form. These reactive forces are the ones that will move the teeth.

Many specialists are wrong in trying to understand and explain the law of action and reaction in orthodontics. Some of them refer to Newton’s third law in order to understand anchorage questions. For example, if you consider a simple anterior retraction, in which the orthodontist wishes to retract the incisors without mesial movement of the posterior teeth (the so-called loss of anchorage). Many professionals refer to the force applied to the incisors as an action force, while the posterior teeth would receive the reaction forces. In fact, this interpretation is incorrect. It is not the Newton’s third law that supports this statement. In this case, we should use the term DESIRED to describe the force on the incisors, and the term UNDESIRED to describe the force on the molars. The two are equal and opposite, but they DO NOT represent the forces of action and reaction described by Newton. The interaction between action and reaction when we insert an appliance between two teeth (or two blocks of teeth, as in the example) does NOT occur directly between the two teeth, but between the APPLIANCE and EACH of the teeth, as explained above.

You may have noticed that we did not approach the second law of Newton in this post. This is because the tooth displacements during the orthodontic movement depends on complex biological responses which take days to occur, and they can not be accurately predicted by any formula of physics. At the moment we apply a force to the teeth, they suffer a minimum acceleration due to elastic deformation of the periodontal ligament, but the restriction induced by the ligament quickly places the teeth in rest position – YES, the teeth will also be in equilibrium (the force systems are counterbalanced by the forces of the ligament)! This does not mean that the teeth will not move. Remember that different strains on ligament will trigger specific biological responses (eg. bone modeling and remodeling), and these responses will allow the tooth movement.

Final Considerations and Clinical Applications

We end this post claiming your attention to the importance of using the correct terms in order to study the first and third law of Newton. They form the basic mechanics of tooth movement, and the appropriate understanding of these laws will be essential in order to go depth into the scientific principles of orthodontic biomechanics.

Since the forces that we are interested are the reactive forces (deactivation forces), how can we predict them accurately?… Obviously, we FIRST need to identify the activation forces induced on the appliances. And how can we identify these forces? … Respecting the principle of EQUILIBRIUM. If ALL appliances are in equilibrium at the moment of activation, we should be able to find and recognize the force systems responsible for this equilibrium. The equilibrium should not be created. It is already there. It is a principle, a law, there are no exceptions!! The principles apply in ALL possible and imaginable situations. This means that the correct interpretation and application of these laws can significantly optimize our clinical life.

In the next post we will explain how to assess if an appliance is in equilibrium (it must be!). The complexity of the matter did not allow us to finalize the issue in only one post.

Do not miss Part 2: How to assess the equilibrium of any appliance?