| II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. In this law the direction of the force is the same as the direction of the acceleration. |
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.
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). Aristotle's view seems to be more in accord with common sense because we fail to appreciate the role played by frictional forces. Once an account is taken of all forces, the dynamics of Galileo and Newton, not of Aristotle, are 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!).
Where does the story of the apple come in?
Perhaps like this: Newton, upon
observing an apple fall from a tree, began to think along the following
lines: The apple is accelerated, since its velocity changes from zero as it is
hanging on the tree and moves toward the ground. Thus, by Newton's 2nd
Law there must be a force that acts on the apple to cause this acceleration.
Let's call this force "gravity", and the associated acceleration the
"acceleration due to gravity".
What would be the limit of this "acceleration due to gravity"? Could it, would it, extend to the moon? This was Newton's true insight: the orbit of the Moon about the Earth could be a consequence of this gravitational force.