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# 01. Concepts and Principles

### Newton's Laws

#### 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, but that 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.

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

#### 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:

The capital Greek letter sigma, S, is used as a shorthand to remind you to sum all of the forces acting on the object. 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 in magnitude to the force that the second object exerts on the first. To speak of one object as exerting a force on another is to speak of only one-half of the picture. This idea, known as Newton’s Third Law of motion, is of central importance in the study of forces. In summary, objects interact with each other, and equal magnitude forces are exerted on each of the two objects interacting. A simplistic way of picturing this is the idea that you cannot touch something without being touched, and moreover, that the harder you touch, the harder you will be touched in return.

Investigating the dynamics of a situation involves the identification of all interactions an object experiences with other objects in its surroundings. To help in the identification of these interactions, and to use this information to better describe the ultimate motion of the object, a number of useful analysis tools are detailed below.

Forces come in pairs and are always equal in magnitude, but opposite in direction