# 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:

 $\ds \mathbf F$ $=$ $\ds \dfrac {\d \mathbf p} {\d t}$ 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.

## Source of Name

This entry was named for Isaac Newton.