Physics Corner: Eyes on Newton

Newton's Three Laws of Motion

Let us begin our explanation of how Newton changed our understanding of the
Universe by enumerating his Three Laws of Motion.

Newton's First Law of Motion:

I. Every object in a state of uniform motion tends to remain in that state
of motion unless an external force is applied to it.

This we recognize as essentially Galileo's concept of inertia, and this is often
termed simply the "Law of Inertia".

Newton's Second Law of Motion:

II. The relationship between an object's mass m, its acceleration a, and
the applied force F is F = ma. Acceleration and force are vectors (as
indicated by their symbols being displayed in slant bold font); in this
law the direction of the force vector is the same as the direction of the
acceleration vector.

This is the most powerful of Newton's three Laws, because it allows quantitative
calculations of dynamics: how do velocities change when forces are applied.
Notice the fundamental difference between Newton's 2nd Law and the dynamics of
Aristotle: according to Newton, a force causes only a change in velocity (an
acceleration); it does not maintain the velocity as Aristotle held.
This is sometimes summarized by saying that under Newton, F = ma, but under
Aristotle F = mv, where v is the velocity. Thus, according to Aristotle there is
only a velocity if there is a force, but according to Newton an object with a
certain velocity maintains that velocity unless a force acts on it to cause an
acceleration (that is, a change in the velocity). As we have noted earlier in
conjunction with the discussion of Galileo, Aristotle's view seems to be more in
accord with common sense, but that is because of a failure to appreciate the
role played by frictional forces. Once account is taken of all forces acting in
a given situation it is the dynamics of Galileo and Newton, not of Aristotle,
that are found to be in accord with the observations.


Newton's Third Law of Motion:

III. For every action there is an equal and opposite reaction.

This law is exemplified by what happens if we step off a boat onto the bank of a
lake: as we move in the direction of the shore, the boat tends to move in the
opposite direction (leaving us facedown in the water, if we aren't careful!).