Newton published his work on mechanics and optics in the book, Philosophiae Naturalis Principia Mathematica. In the Principia, Newton states his three laws of motion:

Law I:
Every body continues in a state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.


Law II:
The change of motion is proportional to the force impressed; and is in the direction of the straight lines in which that force is impressed.



Force = mass x change in velocity

Newton defined a change in velocity as an acceleration. Given this definition, Newton's second law is stated concisely in the more familiar form,

Force = mass x acceleration
or

acceleration = Force / mass

Comments:

The second law gives us a way to define what mass measures. Mass measures the inertia, the resistance to a change in the state-of-motion of an object. A massive object is harder to accelerate (move) than a less massive object. It is easier to push a mosquito than to push an elephant. We define

Mass (inertial) = Force/ acceleration

Law III:

To every action there is always an equal and opposite reaction; or, the mutual actions of two bodies upon each other are always equal and act in opposite directions.

Example:

• rocket

COMMENT

In one form or another, all of Newton's laws have to do with the conservation of the quantity known as linear momentum. This should suggest that this conservation law is important. It is indeed one of the basic tenets of physics on all levels.

Interestingly, there have been experiments where it appeared that the conservation of linear momentum failed. In particular, an experiment in the middle part of this century which studied the decay of certain radioactive elements did not appear to conserve momentum. A nucleus which was initially at rest (i.e., the system had zero momentum) decayed and the momentum of the resultant particles were measured. Surprisingly, based on the momentum of the detected particles, linear momentum was not conserved!! Given this experiment, one could either conclude that conservation of momentum was violated or that some unknown "invisible" particle was produced which carried off the momentum. Because of the reverence with which conservation of momentum was (and is) held, the choice was to suggest that some undetectable particle carried off the momentum!! A particle was invented to preserve the law! In this way, the neutrino was predicted. It was eventually discovered later in the 1950's.