Newton's Laws of Motion/Second Law

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.

• Newton's First Law of Motion
• Newton's Third 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): constant (in physical laws)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Newton's laws of motion