We are now ready to state Newton's three "Laws" of motion, in Newton's own words:
Now, Newton's language was fairly precise, but to our modern ears it sounds a bit stilted and not very concise. We also imagine that, with the benefit of several centuries of practice, we have achieved a clearer understanding of these Laws than Newton himself. Regardless of the validity of this conceit, we like to express the Laws in a more modern form with a little mathematical notation thrown in:
- 1.
- FIRST LAW: Every body continues in its state of rest, or of uniform motion in a right [straight] line, unless it is compelled to change that state by a force impressed on it.
- 2.
- SECOND LAW: The change in motion [rate of change of momentum with time] is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
- 3.
- THIRD LAW: To every action there is always opposed an equal reaction; or, the mutual actions of two bodies are always equal, and directed to contrary parts.
- 1.
- FIRST LAW: A body's velocity [which might be zero] will never change unless and until a force acts on the body.
- 2.
- SECOND LAW: The time rate of chage of the momentum of a body is equal to the force acting on the body. That is,
(5) - 3.
- THIRD LAW: Whenever a force is applied to A by B, there is an equal and opposite reaction force on B due to A. That is,
(6)
where the subscript _{AB} (for instance) indicates the force from A to B.
As long as the mass m is constant^{7}
we have
(7) |