# Yank (physics)

In physics, yank is sometimes used to denote the derivative of force with respect to time or mass multiplied by jerk. In relativistic physics, it is expressed as the second derivative of momentum with respect to time, because the mass is velocity-dependent. Though not universally accepted as an official term for this quantity, the term "yank" is commonly used among physics enthusiasts.Fact|date=April 2008

Yank is described by the following equation::$mathbf\left\{Y\right\}=frac\left\{mathrm\left\{d\right\}^2mathbf\left\{p\left\{mathrm\left\{d\right\}t^2\right\}=frac\left\{mathrm\left\{d\right\}^2\left(mmathbf\left\{v\right\}\right)\right\}\left\{mathrm\left\{d\right\}t^2\right\}=mfrac\left\{mathrm\left\{d\right\}^2mathbf\left\{v\left\{mathrm\left\{d\right\}t^2\right\}+mathbf\left\{v\right\}frac\left\{mathrm\left\{d\right\}^2m\right\}\left\{mathrm\left\{d\right\}t^2\right\}+2frac\left\{mathrm\left\{d\right\}mathbf\left\{v\left\{mathrm\left\{d\right\}t\right\}frac\left\{mathrm\left\{d\right\}m\right\}\left\{mathrm\left\{d\right\}t\right\}$where:$mathbf\left\{p\right\}$ is momentum:$m$ is mass:$mathbf\left\{v\right\}$ is velocity:$t$ is timeNote that when mass is constant (as in non-relativistic physics), the equation reduces to the following::$mathbf\left\{Y\right\}=frac\left\{mathrm\left\{d\right\}^2mathbf\left\{p\left\{mathrm\left\{d\right\}t^2\right\}=mfrac\left\{mathrm\left\{d\right\}^2mathbf\left\{v\left\{mathrm\left\{d\right\}t^2\right\}$

The units of yank are force per time, or equivalently, mass times length per time cubed; in the SI unit system this is kilogram metres per second cubed (kg·m/s3).

References

* [http://arxiv.org/abs/math-ph/0206038 Yank and Hooke's Constant Group] — "It has been proposed [http://math.ucr.edu/home/baez/physics/General/jerk.html 6] that yank and tug be respectively the rate of change of force and the rate of change of yank".
** [http://math.ucr.edu/home/baez/physics/General/jerk.html UCR Mathematics] — "So far yank (symbol Y) has been suggested for rate of change of force"

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