Newton's Laws of Motion and Physics Concepts

Introduction to Physics Concepts and Newton's Laws

• A review of basic physics concepts is essential before application in clinical cases
• Newton's three laws explain the effects of forces on an object

Newton's Three Laws

• The laws describe the motion of an object subjected to forces
• The Second and Third Laws are most relevant in dentistry

First Law

• In the absence of friction, objects remain at rest or in uniform motion in a straight line unless acted upon by a force
• It defines inertia as a body's reaction or resistance to movement when a force acts upon it
• Inertia describes if the body continues in a state of rest
• Or inertia describes if an object continues in a state of uniform motion in a straight line

Second Law

• The acceleration of a body is in the direction of the applied force
• Acceleration depends on the force's magnitude and the object's mass
• Formula: F = m x a (Force equals mass times acceleration)

Third Law

• For every action or force, there is an equal and opposite reaction force
• When two objects interact, they exert action and reaction forces on each other
• These forces are vectors with magnitude and direction
• The force size on the first object equates the force size on the second object
• The direction of the force on each object is opposite

Application of Action-Reaction

• When a car's wheels turn, they exert a force on the road
• The road exerts an equal and opposite force on the wheels
• The wheels, in effect, push the road backwards, and the road propels the wheels (and hence the car) forwards

Action-Reaction in Canine Retraction

• Using a spring to pull a canine back applies a force
• If molars are used as anchorage, an equal and opposite force pulls the molars forward
• This can cause an undesirable side effect
• Treatment planning should account for and minimize these side effects

Concept of Force

• Force Definition: Any action changes an object's motion
• Forces are quantified in ounces, grams, or Newtons; grams are commonly used in orthodontics.
• Force as a Vector: Direction is represented by an arrow pointing in the tooth's movement direction, magnitude by the arrow's length.
• Point of Application: Location where force is applied to the object
• It is conventionally the arrow's origin and relates to the center of mass
• This location influences the object's translation or rotation tendencies

Line of Action

• Definition: Geometric representation of the applied force
• It is the displacement axis when force is applied
• The arrow indicates the direction, and magnitude (force applied) is the length
• Two forces can be of equal strength, in the same line acting upon a solid has the same impact
• With one directing and the other pulling, the net outcome remains identical

Law of Transmissibility of Force

• The effect of a force remains the same anywhere along its line of action
• For example, force applied to any part of the tooth, long axis remains consistent
• Incisal edge, bracket, or cingulum, will have the same affect, with unchanging magnitude and direction
• Forces of the same magnitude and in the same direction have the same effect, regardless of application point along the line of force
• Scalars describe forces (magnitude only), while vectors describe magnitude and direction (used in free body diagrams).
• Rigid Bodies definition: Solid structures do not change form when affected by compression and tension

Center of Mass

• This is the balance point of a system
• Equilibrium Point: The center indicates a point of zero distribution of mass (forces) with no acting forces
• Force Application: If a guided force pushes through an object it will move without rotation and pure translation will occur

Center of Resistance (CR)

• Tooth roots are secured by alveolar bone through the use of periodontal ligaments to keep them from falling out
• CR is the place where the resistance displacement meets; is located more apically compared to the center of mass
• Mathematical Point: The locus of concentration and applied force
• Clinical Application: CR varies depending on the tooth and how much support and pressure the periodontal provides when applied

Factors Influencing Center of Resistance

• It considers ALL forces acting on an object including the periodontal ligament (PDL), blood vessels, bone, and connective tissue.
• A connected segment of teeth anchored, creates a single solid resistance unit
• Clinical Significance: Applied force measurements determine the course and movement caused by the teeth's resistance on the force
• Periodontal Support: The extent of the alveolar shifts the CR toward the apex (root) if there is bone loss; it is the same with distance from the bracket
• Applying the same pressure, from different points will yield different movements
• The center moves apically when there is great bone loss or teeth shifting occurs

Center of Resistance in Single Tooth

• Resistance, supported by PDL and dentoalveolar bones, helps place the mass
• Clinical Application is tough to perfect as it cannot be defined for all teeth and patients
• The theoretical concept is that is is consistent and helps optimize for force systems

Variance in Resistance

• If the supporting peridontium is constant, the teeth's resistance will be varied accordingly
• Upper canines have greater support, unlike upper incisors
• Position is determined by alveolar bone height and is more prominent in a child vs an adult with periodontal disease

Tooth Alignment Forces

• In cases the periodontal support even and consistent, the teeth will resist the force of power from the point
• The force will translate and move at the site where the teeth meet and brackets secure causing displacement

Combination of Forces

• Dentistry uses the force to determine the force from three main plains and areas; using the parallelogram rule.
• Net Force, with vector summing and vector capabilities, determine the magnitude to control movement
• Parallelogram vectors (F1 and F2) can calculate the magnitude of force and the direction from which it moves accurately

Vector Magnitude Calculation

• The formula: Fr = F1 + F2
• The law to calculate the magnitude in effect is Fr = √F12 + F22 +2F1F2 cos β

Free Body Diagrams

• These are helpful in determining the various effects of each force acting within the body (also known as net force)
• Clinical Use: Intrusion arch and elastatics

Explore fundamental physics concepts and Newton's three laws of motion, which describe how forces affect objects. The laws explain inertia, acceleration relative to force and mass, and action-reaction forces. The Second and Third Laws are particularly relevant in the field of dentistry.