Yank (physics)

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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.^{[citation needed]}

Yank is described by the following equation:

$\mathbf{Y}=\frac{\mathrm{d}^2\mathbf{p}}{\mathrm{d}t^2}=\frac{\mathrm{d}^2(m\mathbf{v})}{\mathrm{d}t^2}=m\frac{\mathrm{d}^2\mathbf{v}}{\mathrm{d}t^2}+\mathbf{v}\frac{\mathrm{d}^2m}{\mathrm{d}t^2}+2\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}\frac{\mathrm{d}m}{\mathrm{d}t}$

where

$\mathbf{p}$ is momentum

m

is mass

$\mathbf{v}$ is velocity

t

is time

Note that when mass is constant (as in non-relativistic physics), the equation reduces to the following:

$\mathbf{Y}=\frac{\mathrm{d}^2\mathbf{p}}{\mathrm{d}t^2}=m\frac{\mathrm{d}^2\mathbf{v}}{\mathrm{d}t^2}$

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).

[edit] References

Yank and Hooke's Constant Group — "It has been proposed 6 that yank and tug be respectively the rate of change of force and the rate of change of yank".
- UCR Mathematics — "So far yank (symbol Y) has been suggested for rate of change of force"