The coefficient of restitution (COR), also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. It is measured in the Leeb rebound hardness test, expressed as 1000 times the COR, but it is only a valid COR for the test, not as a universal COR for the material being tested.
The value is almost always less than one due to initial translational kinetic energy being lost to rotational kinetic energy, plastic deformation, and heat. It can be more than 1 if there is an energy gain during the collision from a chemical reaction, a reduction in rotational energy, or another internal energy decrease that contributes to the post-collision velocity.
Coefficient of restitution
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e
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=
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Relative velocity after collision
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Relative velocity before collision
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{\displaystyle {\text{Coefficient of restitution }}(e)={\frac {\left|{\text{Relative velocity after collision}}\right|}{\left|{\text{Relative velocity before collision}}\right|}}}
The mathematics were developed by Sir Isaac Newton in 1687. It is also known as Newton's experimental law.