*Newton's three laws of motion* may be stated as follows:

- Every object in a state of uniform motion will remain in that
state of motion unless an external force acts on it.
- Force equals mass times acceleration [
].
- For every action there is an equal and opposite reaction.

The first law, also called the *law of inertia*, was pioneered by
Galileo. This was quite a conceptual leap because it was not possible
in Galileo's time to observe a moving object without at least some
frictional forces dragging against the motion. In fact, for over a
thousand years before Galileo, educated individuals believed
Aristotle's formulation that, wherever there is motion, there is an
external force producing that motion.

The second law, , actually implies the first law, since when (no applied force), the acceleration is zero, implying a constant velocity . (The velocity is simply the integral with respect to time of .)

Newton's third law implies *conservation of momentum*
[138]. It can also be seen as following from the
second law: When one object ``pushes'' a second object at some
(massless) point of contact using an applied force, there must be an
equal and opposite force from the second object that cancels the
applied force. Otherwise, there would be a nonzero net force on a
massless point which, by the second law, would accelerate the point of
contact by an infinite amount.

In summary, Newton's laws boil down to
. An enormous quantity
of physical science has been developed by applying this
simple^{B.1} mathematical law to different physical
situations.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University