# Newton's Law

## Disambiguation

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Newton's Law may refer to:

### Newton's Law of Universal Gravitation

Let $a$ and $b$ be particles with mass $m_a$ and $m_b$ respectively.

Then $a$ and $b$ exert a force upon each other whose magnitude and direction are given by Newton's Law of Universal Gravitation:

$\mathbf F_{a b} \propto \dfrac {m_a m_b {\mathbf r_{b a} } } {r^3}$

where:

$\mathbf F_{a b}$ is the force exerted on $b$ by the gravitational force on $a$
$\mathbf r_{b a}$ is the displacement vector from $b$ to $a$
$r$ is the distance between $a$ and $b$.

### Newton's Law of Restitution

Let two solid bodies $B_1$ and $B_2$ be in collision.

Let the components of the relative velocities of $B_1$ and $B_2$ in the direction of their common normal be respectively:

$\mathbf u_1$ and $\mathbf u_2$ before the collision
$\mathbf v_1$ and $\mathbf v_2$ after the collision.

Then:

$\mathbf v_2 - \mathbf v_1 = -e \paren {\mathbf u_2 - \mathbf u_1}$

where $e$ the coefficient of restitution.

### Newton's Laws of Motion

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

## Source of Name

This entry was named for Isaac Newton.