4 Dynamics
Dynamics
Concepts and Principles
Newton’s First Law
Dynamics is the study of the cause of motion, or more precisely the cause of changes in motion. In the late 1600’s Isaac Newton hypothesized that motion does not require a cause, rather changes in motion require causes. An object experiences a change in motion only when it interacts with some aspect of its surroundings. This bold hypothesis, referred to as Newton’s First Law of Motion, is summarized by the idea that an object will maintain its state of motion, whether at rest or traveling at high speed, unless acted upon by some aspect of its surroundings.
Using the kinematic terminology developed in the last unit, this means that an object’s velocity (state of motion) is constant unless it interacts with some outside agent. An external interaction is not necessary for an object to move, it is only necessary if the object’s velocity changes. Thus, what is caused is not velocity, but acceleration. This concept is one of the most subtle, and complex, in all of physics.
Newton’s Second Law
Newton also hypothesized that the sum total of all interactions with the external environment, which he termed forces, is directly proportional to the acceleration of the object. Moreover, the proportionality constant between the sum of all forces acting on an object and the acceleration of the object measures the “resistance” of an object to changes in its motion. This resistance to changes in motion is termed the inertia.
For example, an object with great inertia (quantified by a large proportionality constant) responds to the application of forces with a relatively small acceleration. An object with little inertia (a small proportionality constant) responds to the application of the same forces with a relatively large acceleration. The amount of inertia an object has is measured by the inertial mass of the object.
In summary, this relationship, known as Newton’s Second Law of Motion, and can be written mathematically as:
where
- F is a force acting on the object from its surroundings, measured in Newtons (N),
- S (sigma) is a shorthand reminder to sum all of the forces acting on the object,
- and m is the mass of the object, measured in kilograms (kg).
The sum of all of the forces acting on an object will be referred to as the total force acting on the object.
Newton’s Third Law
Newton’s third great contribution to the study of dynamics was his vision of force, defined to be the interaction between an object and some aspect of its surroundings. Newton theorized that since objects interact with other objects in their surroundings, always in pairs, a certain symmetry exists in nature. The distinction between the actor and the acted-upon is arbitrary. It would be just as easy to switch focus and consider the object in the surroundings as the acted-upon and the original object of interest the actor.
If nature exhibits this symmetry, then the force that one object exerts on another must always be equal i