# Newton's Laws of Motion/Second Law

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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:

- $\mathbf F = \map {\dfrac \d {\d t} } {m \bsv}$

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

This law is also often referred to as just **Newton's second law**.

## 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: $(2)$ - 1966: Isaac Asimov:
*Understanding Physics*... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $3$: The Laws of Motion: Mass - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 1$: Introduction: $(1)$ - 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 - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World: Newton - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**constant**(in physical laws) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Newton's laws of motion**