Yank (physics)

In physics, yank is the derivative of force with respect to time. Expressed as an equation, yank Y is:

$\mathbf{Y}=\frac{\mathrm{d}\mathbf{F}}{\mathrm{d}t}$

where F is force and $\frac{\mathrm{d}}{\mathrm{d}t}$ is the derivative with respect to time $t$.

The term yank is not universally recognized but is commonly used.^{[citation needed]} 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), or Newtons per second (N/s).

Relation to other physical quantities

Newton's second law of motion says that:

$\mathbf{F}=\frac{\mathrm{d}\mathbf{p}}{\mathrm{d}t}$

where p is momentum, so if we combine the above two equations:

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

where $m$ is mass and v is velocity. If the mass isn't changing over time (i.e. it's constant), then:

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

which can also be written as:

$\mathbf{Y}=m\mathbf{j}$

where j is jerk.

See also

• Tug
• Jerk