# Newton's Laws of Motion/Second Law

< Newton's Laws of Motion(Redirected from Newton's Second Law of Motion)

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## Physical Law

**Newton's Second Law of Motion** is one of three physical laws that forms the basis for classical mechanics.

### Statement of 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 |

## Also presented as

**Newton's Second Law of Motion** is also seen presented in the form:

\(\ds \mathbf F\) | \(=\) | \(\ds m \dfrac {\d \mathbf v} {\d t}\) | ||||||||||||

\(\ds \) | \(=\) | \(\ds m \mathbf a\) | where $\mathbf a$ denotes acceleration |

which is not its most general form, as it assumes constant mass.

Indeed, as Isaac Newton himself put it:

*The acceleration produced by a particular force acting on a body is directly proportional to the magnitude of the force and inversely proportional to the mass of the body.*

## Also known as

**Newton's Second Law of Motion** is also often referred to as just **Newton's Second Law**.

Some refer to it as just **Newton's Law**, on the grounds that it is the most significant of all of **Newton's Laws of Motion**, but there is more than one of those.

## Also see

- At velocities near the speed of light, see Einstein's Law of Motion.

## Source of Name

This entry was named for Isaac Newton.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1965: J.W. Leech:
*Classical Mechanics*(2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Introduction: $(2)$ - 1977: A.J.M. Spencer:
*Engineering Mathematics: Volume $\text { I }$*... (previous) ... (next): Chapter $1$ Ordinary Differential Equations: $1.1$ Introduction - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.7$: A Simple Approach to $E = M c^2$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.8$: Rocket Propulsion in Outer Space - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**force** - 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):**force** - 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**