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{excerpt}An interaction which produces a change in the motion of an object.{excerpt}

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h2. Motivation for Concept

Consider a bowling ball (or some other heavy object).  If you want the ball to move, you have to interact with it.  If you want the moving ball to turn, you have to interact with it.  If you want the ball to stop moving, you have to interact with it.  In physics, such interactions are called forces.  If you want to move the ball, you will probably have to apply a contact force by using your hands or feet.  There are other kinds of forces, however.  The earth, for example, can alter the ball's motion through the invisible action-at-a-distance of gravity.  

h2. Statement of Newton's Laws

Newton's famous Three Laws form the basis of a scientific understanding of force.

h4.  First Law

[Newton's First Law] describes what happens in the _absence_ of forces.  If an object is moving with no force acting upon it, then it will move with constant [velocity].  Note that velocity is a vector, so this statement implies that the object will keep the same speed *and* the same direction of motion.  

h4.  Second Law

[Newton's Second Law] defines force as the time rate of change of [momentum]:

{latex}\begin{large}\[ \vec{F} \equiv \frac{d\vec{p}}{dt}\]\end{large}{latex}

If many forces act upon an object, then the change in the object's momentum is equal to the combined effect of all the forces:

{latex}\begin{large}\[ \sum_{k=1}^{N_{F}} \vec{F}_{k} = \frac{d\vec{p}}{dt} \] \end{large}{latex}

{note}It is important to note that the sum is _only_ over forces that act *on the object* whose momentum change appears on the right hand side.{note}

In most cases, the object under consideration will have a constant mass.  If that is so, then the derivative of the momentum can be rewritten in the _traditional formulation_ of Newton's Second Law:

{latex}\begin{large}\[ \sum_{k=1}^{N_{F}} \vec{F}_{k} = ma \]\end{large}{latex}

This form of the equation is the basisfundamental Law of Interaction for the [Point Particle Dynamics] model.


h4. Third Law

[Newton's Third Law] is a rule for determining the effects of forces.  This Law states that whenever one object applies a force on a second object, the second object *must* apply a force of the same size but opposite direction on the original object.  

{warning}This law is often misunderstood.  The wording makes it seem that forces are always a choice, but this is certainly incorrect.  Objects apply forces without _choosing_ to all the time.  This law is simply describing well known consequences of action.  Trying to change the motion of a bowling ball with a swift kick is a dangerous idea, because the bowling ball will automatically push back on your foot.  Trying to tackle a 200 pound athlete running at full speed is going to hurt, even if they do not purposely push against you.{warning}

h2. Types of Forces

Newton's Laws describe the consequences of forces and give the rules they must obey, but the laws do not explain the types of forces that can be exerted.  There are a vast array of ways for objects to interact with each other, but the ways that are commonly treated in introductory physics courses is a rather short list:

# [contact forces|contact force] occur when one rigid body comes in contact with another.
# [gravity] is the attraction at a distance between massive objects.  In introductory physics, we most often consider the force of gravity exerted by the earth on objects near its surface, in which special case the force is usually called [weight].
# [normal forces|normal force] are a special case of contact force when an object is moving along a surface like a floor, ceiling or wall.  The normal force is the portion of the contact force applied to the object by the surface that is directed perpendicular to the plane of the surface.
# [tension] is a force exerted by a string or rope.  
# [friction] is a force exerted by a surface on an object moving along (or at rest on) that surface that is directed parallel to the plane of the surface.

h2. Application of Newton's Laws

h4. Physical Representation

Before setting up the equations of Newton's Second Law for an object, it is vital to quantitatively understand the forces acting on the object.  The first step is to draw a [physical representation] of the situation.  Here is an example:

PHYSICAL REP

This example shows a box that is acted upon by each of the five common categories of forces in introductory physics.  The person pushing the box applies a contact force _F_~p~.  (The subscript "p" is chosen here to denote "push".  You might also use "a" for applied, "c" for contact, or any other subscript that has meaning for you.)  The person in front pulls on a rope, which transmits a tension force _T_ to the box.  The earth's gravity gives the box a weight force _W_.  The floor provides both a normal force _N_ and a friction force _F_~f~.

h4. Free Body Diagram

This physical representation is not very useful as a guide to using the equations of Newton's Second Law.  If we wish to write Newton's 2nd Law algebraically, it is important to find the components of each vector.  An alternate graphical representation that leads naturally to finding the vector components is the [free body diagram].  In a free body diagram, the center of mass of the box is represented as a point at the origin of a coordinate system.  All the forces acting on the box are then drawn as [vectors|Introduction to Vectors] with their [tail] at the origin.  For the example of the box, the free body diagram would be:

FBD

which leads naturally to the resolution into components:

COMPONENTS

h4. Writing Newton's 2nd Law