we get to Newton's laws, we probably should take a moment to
define what a law is. 0
"Professor Goddard does
not know the relation between action and reaction and the need
to have something better than a vacuum against which to react.
He seems to lack the basic knowledge ladled out daily in high
York Times editorial opinion about Robert Goddard's
revolutionary rocket work.
The Times printed
an apology the day after Apollo 11 lifted off for the Moon.
"Further investigation and experimentation have confirmed
the findings of Isaac Newton in the 17th century, and it is now
definitely established that a rocket can function in a vacuum
as well as in an atmosphere. The Times regrets the error."
A law in science
is a statement
of how nature
Always means always. Should we find
an exception to the rule, we do not discount the exception; rather,
we modify, even discard if necessary, the law to take into account
the new knowledge.
We will spend considerable time dealing with how things move
and why they move (or don't move) the way that they do. 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.) The reader should note that
the numbering of the three laws is important. All through the
literature, reference is made to a given law by number.
The First Law
Every body continues in its state of
or of uniform motion in a straight line,
unless it is compelled to change that state
by forces impressed upon it.
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 reference
to giants printed elsewhere on this site; 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. He came to this conclusion while
analyzing the motion of a ball rolling down an inclined plane.
It was a simple enough experiment. He released the ball so that
it rolled down the left incline and across the level surface.
When it reached an identical incline on the other side, the ball
traveled up the plane, stopping at the same level as that from
which it was released. As he lowered the angle of the receiving
incline, the ball still stopped at the starting height even though
it had a greater distance to travel. Galileo suggested that if
the receiving plane were not inclined at all, the ball would
continue forever trying to reach the original starting height
The first law suggests what happens
when the forces acting on a object cancel out, when 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. The object is said to be in equilibrium
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
= 0 for that object. On the other hand, should we find a situation
where it is speeding up, slowing down or not moving in a straight
line, we should conclude that Fnet is not equal to zero and start
searching for the cause of the unbalanced force. When viewed
in this light, the realization that the moon is not traveling
in a straight line path means that some force is acting on it
to chance its path just seems to fit.
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 = S Forces. In the case
of the first law Fnet = S Forces = 0.
See an equilibrium problem here.
The Second Law
Whenever an object accelerates, the
a) directly proportional to the NET force
acting on the object;
b) pointing in the same direction as the net
c) inversely proportional to the mass of the
If the first law describes the situation
= 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 /s2, then the unit for force will be the kg-m/s2.
This quantity is now renamed the Newton and
will be the (nearly) exclusive unit of force used at this site.
For comparison sake, there are about 4.45 N in one pound. What
is left of a quarter pound beef pattie after cooking weighs about
one Newton. What is your weight in Newtons?
F = ma raises for the first time the
matter of derived units.
Certain quantities in physics such
as mass, length and time (there are seven kin all) are said to
be fundamental and exist by definition. The units used to describe
all other quantities are derived units, expressed as combinations
of the basic stuff. The unit of mass is most commonly the kilogram
(kg), a basic unit; the unit for acceleration is m/s/s, a combination
if basic units.
F = ma suggests that some word we use
to name force must be equal to the units on the other side, namely,
kg m/s/s. This last collection of syllables is a lot to say and
to write. We rename this assembly of units the Newton, abbreviated
N, capital letter for a proper name. We physicists take care
of our own in a very special way. Daily, uncounted numbers of
people doing science pay tribute to Sir Isaac for his good work
by saying his name
See more about units at
A caveat to the student
Under no circumstance should any student believe that
work will be easier because Newton's second law, F = ma, appears
to be so simple. On the contrary, you are about to engage in
the most difficult topic seen to date. In earlier work in kinematics,
all pertinent quantities were related by special equations (see
the equations page). Data (sometimes includimg acceleration)
were given, and the student had to find the missing quantitiy.
No longer will the acceleration be given; instead you will have
to analyse the forces to determine Fnet, and from that you find
a. Not easy
to Newton's laws
The Third Law
every action there is an
equal and opposite reaction.
Newtons 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
comes from the fact that the equal and opposite forces never
cancel each other out because each acts on a different object.
The best example that comes to mind that crystalizes the problem
is that of the reluctamt
horse. The dialog goes
something like this:
A horse is attached to a wagon. The driver says to the horse
" giddyap". The horse replies as follows:
" I was reading
a physics text lasat night and ran across Newton's third law.
It says that 'For every action there is an ezual and opposite
reaction' Thta means that if I pull on the wagon, the wagon pulls
back on me. The forces are equal in magnitude and oppositely
directed. They will cancel each other out so why should I try."
We suspect that there
may be a flaw in the horse's logic. What's the flaw? See the
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 in a high
school course 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--to name
two. The web sites that you visit here should give you some idea
of how these rules are applied.
Return to Newton's
Traffic Outcomes and the First Law
The reader can be reasonably assured
that one will understand the laws of physics when one can walk
though a daily routine and recognize the laws of physics all
around. Automobile drivers and passengers are at serious risk
of bodily harm if they ignore the consequences of Newton's first
law when an accident event presents itself. Consider these negative
traffic outcomes that can occur when the user has no passenger
restraint system in place. Can you see the first law at work
here? Warning: carnage ahead.
- Your car is stopped at a traffic light
and is struck from behind. The most common claim for injury is
"whiplash" But instead of your head being snapped back,
it is your head ("a body at rest." that remains at
rest when your torso is pushed forward.
- Distracted by your cell phone conversation,
you fail to notice that your car is veering off the road and
into a bridge abutment. Your car stops abruptly; absent any restraint
system, you continue "with uniform speed in a straight line"
- It's the dead of winter. You are driving
down a twisty country road that has a sudden sharp turn to the
left. You turn the steering wheel, but to no avail. The road
is ice-covered and your tires have no traction. You continue
"with uniform speed in a straight line" into serious
- Same country road, same curve, same
high rate of speed. There is enough traction between tires and
roadway. The car negotiates the curve, but the driver, without
passenger restraint, slides across the bench seat, through the
passenger door and into trouble, This event , when seen from
above, finds you moving "with uniform speed in a straight
The carnage here could have been significantly
reduced if the vehicles were equipped with some find of passenger
restraint system to prevent automobile passengers from leaving
their seats. Restraint systems fall into two general categories:
passive restraint and active restraint.
- Passive restraint systems will deploy automatically without direct intervention
from the user. Air bags are a passive restraint system; so, too,
are the head rests that reduce whiplash injury.
- Active restraint systems require a conscious decision to deploy the safety
apparatus. Traditional lap belts are of little value if the bucklle
is not secured.
Question: What does one call a person
who ignores all restraint systems?
Answer: Organ donor.
See this page for the legislative history
of seat belt.
The horse's logic revisited
this page was last visited 01/23/09
The horse's logic is correct as far
as it goes. The forces in question are equal in magnitude and
are oppositely directed. They do not cancel because they are
APPLIED TO DIFFERRENT OBJECTS. The horse pulls one the wagon.
The wagon pulls one the horse. The correct reasoning for the
horse shuld be. "When you exert a force on the wagon, friction
sets up a force on
the wagon Those forces are oppositely
directed, if the force applied by friction is greater than that
applied by the horse, the wagon won't move"