Newton's Law of Restitution

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 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
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): coefficient of restitution
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): coefficient of restitution
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