# Newton's Laws of Motion

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## Physical Laws

**Newton's Laws of Motion** are a set of three physical laws that form the basis for classical mechanics.

### First Law

- Every body remains in a state of constant velocity unless it is acted upon by an external unbalanced force.

This of course includes it being stationary, that is, with a constant velocity of zero.

### Second Law

The total force applied on a body is equal to the derivative with respect to time of the linear momentum of the body:

\(\ds \mathbf F\) | \(=\) | \(\ds \dfrac {\d \mathbf p} {\d t}\) | where $p$ denotes linear momentum | |||||||||||

\(\ds \) | \(=\) | \(\ds \map {\dfrac \d {\d t} } {m \mathbf v}\) | where $m$ denotes mass and $\mathbf v$ denotes velocity |

### Third Law

- To every force there is always an equal and opposite force.

- That is, the forces of two bodies on each other are always equal and are directed in opposite directions.

## Also known as

**Newton's Laws of Motion** can also be referred to as just **the Laws of Motion**.

## Source of Name

This entry was named for Isaac Newton.

## Historical Note

**Newton's Laws of Motion** were expounded by Isaac Newton in $1687$ in his *Philosophiae Naturalis Principia Mathematica*.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1966: Isaac Asimov:
*Understanding Physics*... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $3$: The Laws of Motion: Inertia - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Newton's laws of motion** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Newton's laws of motion** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Newton's laws of motion**