# Newton's Law of Restitution

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## Physical Law

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.

## Source of Name

This entry was named for Isaac Newton.

## Historical Note

Isaac Newton stated the **Newton's Law of Restitution** at the same time as **Newton's Laws of Motion**.

He came up with it as a result of experiments.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Newton's law of restitution** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Newton's law of restitution**