Sir Isaac Newton Published The first person to organize this study into a concise package was Isaac Newton. In 1686 he published Philosophiae Naturalis Principia Mathematica, commonly known as the Principia, in which he detailed the rules that govern how things move. The cornerstone onto which the bulk of classical mechanics is built is usually cited as Newton's laws of motion, of which there are three. (Note that the law of universal gravitation is not listed among this set of three statements.)

Newton's First Law

Every body continues in its state of rest,
or of uniform motion in a straight line,
unless it is compelled to change that state
by forces impressed upon it.

Sir Isaac Newton was a great assimilator of ideas, combining his own work with the thoughts of others. It is this aspect of his work that caused him to make the statement printed at the top of this page; in this case, the giant to which he is referring is Galileo, who fell upon the first law while doing inclined plane experiments.

The Greeks had settled on half of the first law by suggesting that an object will not move if no forces are acting upon it. But they went on to say that in order to move at all or to continue moving, a force must be applied continuously. They went to great lengths to explain how a thrown rock would still be pushed by some agent. Galileo reasoned that a moving object would continue moving unless a force was applied to it. Here is one of those situations in science when a step  closer to the truth is taken only when we take current thinking and turn it inside out.

The first law suggests what happens when the forces acting on a object cancel out, upward forces negating downward forces, left negating right. If such conditions exist and the object in question is already at rest, then the object will remain at rest. Similarly, if the object is moving with uniform speed in a straight line and the condition of equal forces exists, the object continues to move with uniform speed in a straight line. The first law suggests that nothing about the motion will change if the forces acting on the object add to zero. A different way to look at the first law is to consider any object at rest or moving with uniform speed in a straight line; such a motion causes us to conclude that Fnet = 0 for that object. The first law is also known as the law of inertia, at Latin word meaning "sluggish" or "unchanging". The term describing the sum of the forces acting on an object is Fnet =  ∑ Forces. In the case of the first law Fnet = ∑ Forces = 0.

Newton's Second Law

Whenever an object accelerates, the acceleration is :

a) directly proportional to the NET force acting on the object;
b) pointing in the same direction as the net force;and
c) inversely proportional to the mass of the object.

If thee first law describes the situation where Fnet = 0, the second law describes what happens when Fnet is not = 0. That is to say, there is acting on the object an unbalanced force that is left uncanceled by anything else. The second law suggests that when such a situation exists, the object is question will accelerate. The acceleration produced this way is directly proportional to Fnet, in the same direction as Fnet, and inversely proportional to the mass of the object. The most common way to write the second law is Fnet = ma. We can say that if Fnet is not = 0, the object in question will accelerate. Alternatively, if we see an object accelerating, i.e., speeding up, slowing  down, or changing direction, we can conclude that there must be some unbalanced force acting on the object and that the unbalanced force acts in the same direction as the acceleration. This fact  can be useful in finding hidden forces that may act on objects. You have already spent considerable time dealing with how things move while working with the previous section on kinematics. The "a" in those equations comes from Newton's second law. A word of caution is in order for the reader. Fnet = ma seems to the simplest equation one could have. You will soon discover that finding Fnet will sometimes be a challenge.

We need to consider the units we will be using for force. From F = ma, if mass is measured in kg and acceleration is measured in m /s^2, then the unit for force will be the kg-m/s^2. This quantity is now renamed the Newton and will be the (nearly) exclusive unit of force used at this site.

Newton's Third Law

For every action there is an equal and opposite reaction.

Newton's third law is the easiest to state and is the one most easily misunderstood. It suggests that if object A pushes on B, then B pushes back on A. The forces are always equal, and always oppositely directed. The misunderstanding come from the fact that the equal and opposite force never cancel each other out because each acts on a different object. The third law is usually applied in the analysis of systems of forces. The word "dynamics" is defined as the study of the forces acting on objects.

The most common forces that we deal with are:

1) gravitational force, the attraction that the Earth has for an object because each (the  object and the Earth) has a mass;

2) normal force, a force exerted on an object by a surface on which the object is resting;

3) applied forces, a push or pull caused by some agent; and 4) frictional force, a force that  tends to oppose motion.

When a situation exists where F net = 0, we often say that the object is in equilibrium. While equilibrium situations are useful in real life, much of our existence deals with change--change in  position and change in velocity.