Almost everyone has heard
of the equation E = mc^{2}. And
indeed this is the most famous equation in physics, establishing
an equivalence between energy and mass. But is
this the most important equation in physics? Knowledgeable scientists
will tell you no. The most important equation in physics is F = ma, also
known as Newton's second law of mechanics. It governs
the behavior of everything that is seen and unseen
on Earth and in the cosmos -- from the
trajectory of a baseball to the motion of a planet.

Students of science and engineering devote
half of the time of a classical mechanics course studying
and learning how to apply this
equation. Thus if you understand F = ma, you know a lot of physics.

Sir Isaac Newton (1642-1727)
The Scientist Responsible for the Most Important Equation
in Physics^{*footnote}

So what does the
equation mean? It can be rewritten in an equivalent
and more intuitively understandable form
as a = F/m. Cast in this way, Newton's second law provides the response
of a body of mass m to a force F. Forces
are things that cause changes
in motion. Such a change is called acceleration and
is denote by the symbol a. A body
is undergoing acceleration if it changes
its speed or changes its direction of motion.

When you push something, you
are inflicting a force
upon it. Hence, if you strike a vase with your hand knocking
it over, the vase feels a force
and undergoes a change of motion. Clearly, a vase
lying on its side has undergone a change in state.

Many equations in all kinds of fields
have the form

(response) = (driving effect)/(resisting effect)

and Newton's second
law is of this structure. Comparing the above to a = F/m, one sees
that the resisting effect
is the mass of an object, which is sometimes called
inertia meaning "the tendency to remain
still." Indeed, it is very hard to change the motion
of a heavy object. Imagine
five people trying to push a car. On the other hand, light
objects are easy to accelerate. You
don't need five physicists to screw in a light bulb.

In the form F = ma, Newtons' second
law tells us the force F needed to implement an acceleration a
on a body of mass m. As explained above, force is
the driving impetus that causes bodies to accelerate. Examples of forces
are gravity, which for example makes things
to fall to the ground and causes the
planets to move around the Sun; friction, which slows down objects
as they rub against another substance; the
electric force, which makes charged bodies
repel or attract each other and is responsible
for the flow of electricity; the magnetic force,
which for examples deflects the needle
of a compass; buoyancy, which makes things
float; and so on. There are countless forces in nature, all
creating changes in movement.

Newton's first law of mechanics says
that, unless acted upon by forces, a body at rest will remain
at rest or a body in motion will remain in motion
moving with the same speed and direction. This first law actually follows
from the second: If F = 0, then a = F/m = 0 also, and if an object
doesn't accelerate then it doesn't change its motion.

A world without forces
would be very dull indeed. All bodies
at rest would remain at rest; all moving objects would
travel at constant speeds in fixed directions forever. There
would be no change in movements. All would be predictable but boringly so.

Summarizing, Newton's second law provides a
mechanical means for determining the motions of objects. To determine
the future movement of a body, one needs to know
its mass m, the force F acting on it and
its current state of motion. Then one
can determine the change in motion about to occur, also known
as its current acceleration a, from a = F/m.

This above discussion is an intuitive introduction
to the most important equation in physics. If you would like to see some
numerical examples, click here.

------------
^{*footnote} Isaac
Newton did not explicitly write down the second law
in the form F = ma: It was actually
Leonhard Euler who expressed it this way.

This webpage was prepared by Dr. Stuart Samuel, who
has given Jupiter Scientific Publishing permission
to use this page
and
who is the spokesperson for
The Bible According to Einstein: A
Scientific Complement to the Holy Bible published
by Jupiter Scientific,
an organization devoted to the promotion of
science through books, the internet
and other means of communication.

This web page may NOT be copied onto other web
sites, but other sites may link to this page.