Skip to content

Yank (physics)

The first time derivative of force, distinguishing how fast a force changes from the force level itself across measured or modeled force trajectories.

Version
v1 · 2026-10-31 · History
Domain-specific #
14599
Domain group
Natural Sciences
Origin domain
Physics
Subdomain
Force Time Analysis → Physics
Aliases
Force yank

Core Idea

Yank is the first time derivative of force: for a differentiable force trajectory \(\mathbf F(t)\), \(\mathbf Y(t)=d\mathbf F(t)/dt\). It reports how fast and in what direction the force vector changes at an instant, rather than how large the force is. For a measured scalar component, such as vertical ground-reaction force, the component derivative has a sign relative to that chosen direction. A positive or negative peak in that component can mark a rapid rise or fall while the force itself remains nonzero.[1]

The name was proposed for the force derivative in a 2019 biomechanics Commentary, which expressly noted that it was not then a standard term throughout physics.[1] Later studies use the same named quantity for different force records. Sahrom and colleagues derive a vertical yank trace from force-platform data to examine countermovement-jump events.[2] Jiang and colleagues estimate the derivative of grasp force and compare it with cortical activity during hand grasp.[3] Those are uses of one force-typed metric, not evidence for a universal neural or movement mechanism.

An exact derivative belongs to a differentiable model. Real force records are sampled and noisy, so a computed yank trace is an estimate whose sampling, filtering and component choice must be stated. A two-point rate of force development over an interval is an average rate, not automatically the instantaneous derivative.[1]

How would you explain it like I'm…

How Fast a Push Changes

When you push a swing, your push can get stronger or weaker. Yank tells you how fast your push is changing, not how hard you're pushing. You can still be pushing hard while the yank says your push is quickly getting weaker.

How Fast a Force Changes

A force is a push or a pull. Yank (physics) tells you how fast a force is changing at a moment, and in which direction, rather than how strong the force is. For example, when you jump, the floor pushes up on you, and yank shows when that push is rising quickly or dropping quickly, even while the floor is still pushing. The name was suggested by scientists who study body movement, and it isn't yet a standard word everywhere in physics. Because real measurements are a bit bumpy, scientists have to say how they calculated it.

Time Derivative of Force

Yank (physics) is the rate of change of force over time, Y = dF/dt. It describes how fast and in what direction the force vector is changing at an instant, not how large the force is. For a single measured direction, like the vertical force from the ground during a jump, yank can be positive or negative, marking a fast rise or fall while the force itself is still nonzero. The name was proposed in a 2019 biomechanics paper, which noted it wasn't yet standard across physics; later studies used it for jump force data and for grip force compared with brain activity. Since real force data are sampled and noisy, a computed yank is an estimate, and a rate measured between two points over an interval is an average, not the instantaneous value.

 

Yank (physics) is the first time derivative of force: for a differentiable force trajectory F(t), Y(t) = dF/dt. It reports the instantaneous rate and direction of change of the force vector, not the force's magnitude. For a chosen scalar component, such as vertical ground-reaction force, the component derivative carries a sign relative to that direction, and a positive or negative peak can mark a rapid rise or fall while the force remains nonzero. The term was proposed for the force derivative in a 2019 biomechanics Commentary, which noted that it was not then standard throughout physics. Later work applies the same metric to different force records: Sahrom and colleagues derived vertical yank from force-platform data to study countermovement-jump events, and Jiang and colleagues estimated grasp-force derivatives and compared them with cortical activity. These are uses of one force-derived metric, not evidence of a universal neural or movement mechanism. An exact derivative belongs to a differentiable model; measured records are sampled and noisy, so a yank trace is an estimate whose sampling, filtering and component choice must be stated, and a two-point rate of force development over an interval is an average rate, not automatically the instantaneous derivative.

Structural Signature

  • Force trajectory. A force vector \(\mathbf F(t)\), or an explicitly named measured component, changes with time. A single force value does not determine yank.[1]
  • First time derivative. The operation \(d\mathbf F/dt\) turns the force trajectory into a local change rate where the derivative exists. Integrating force instead gives impulse, not yank.[1]
  • Vector or component readout. Vector yank has direction; the derivative of a selected scalar component has a sign relative to its chosen axis. One measured component cannot reconstruct unmeasured components.[1][2]
  • Empirical estimate. Sampled force requires a differentiation rule and often filtering. The result is an estimate of the mathematical derivative; noise and temporal resolution affect its peaks.[1][2][3]
  • Task-specific interpretation. A jump-event marker or a correlation with cortical-band power is a use of yank, not part of its definition. Those inferences require their own evidence.[2][3]

The first two roles constitute the quantity. The remaining roles control what an observed or modeled trace can legitimately say.

What It Is Not

  • Not force level. Two instants can have the same force while their local force-change rates differ. A plateau can have appreciable force and little yank.[3]
  • Not every rate of force development. A force increment divided by a nonzero time interval is an average over that interval. Under suitable smoothness it averages pointwise yank, but it need not equal yank at either endpoint.[1]
  • Not automatically a full vector measurement. Sahrom's vertical force-plate trace and Jiang's scalar grip-force trace yield component or scalar estimates. Neither alone determines the unrecorded vector components.[2][3]
  • Not automatically jerk multiplied by mass. If the relevant force is \(m\mathbf a\) with constant \(m\), its derivative is \(m\,d\mathbf a/dt\); different force models or variable mass do not license that shortcut.[1]
  • Not a causal account of sensing. A cortical signal correlated with force yank does not prove that neural activity encodes yank generally or that yank caused the activity.[3]

Scope of Application

Yank applies wherever a force can be represented as a sufficiently regular function of time. In biomechanics it can summarize rapid changes in ground-reaction, muscle, tendon or grasp force. The original Commentary argues for using the same derivative across those force carriers, while explicitly distinguishing a continuous quantity from estimates obtained from particular measurements.[1]

The two studied habitats here are narrower. In countermovement jumping, researchers filtered force-platform recordings, estimated the derivative of vertical force, and rectified and smoothed the signal for event analysis. Their study compared selected events with synchronized motion and electromyography; it did not establish that every jump phase can be identified from yank alone.[2] In hand grasp, researchers estimated scalar grasp-force yank during onset, hold and offset and compared its time course with electrocorticographic band-power changes in four patients.[3]

The mathematical derivative can be defined for a modeled force without an instrument. Claims about measured peaks, their timing, or their biological meaning require the measurement procedure and a task-specific validation. A generic derivative of position, price or stress is not yank unless the differentiated quantity is force.

Clarity

The name separates how much force exists from how quickly that force is changing. During a sustained grasp, force can remain above baseline while the transient yank signal falls back toward zero; Jiang and colleagues compare both time courses rather than treating them as interchangeable.[3] For a jump, a change in the slope of the vertical force trace may be visible in the derivative before it is obvious from force magnitude alone.[2]

It also makes the reporting unit explicit. A vertical force derivative is tied to the vertical axis; Sahrom and colleagues rectify its estimate for their event analysis, removing the sign that otherwise distinguishes rising from falling force.[2] A pointwise derivative differs from an interval rate of force development.[1] Those choices change what the reported trace means.

Manages Complexity

A force record may contain onset, a rise, a plateau, reversal and relaxation. Yank compresses that time course into a change-rate trace, drawing attention to transitions rather than absolute load. Sahrom and colleagues used this compression to seek specific jump events from a force plate when full motion capture is less convenient; Jiang and colleagues used it as a time-varying comparator for cortical activity during grasp onset and release.[2][3]

The compression discards information. A derivative alone does not recover the original force level without an initial condition. Sahrom and colleagues rectify their component-derivative estimate, which removes its original sign.[2] Numerical differentiation may magnify sensor noise,[1] while filtering can make the estimate more stable and may blur real, short transitions. The analyst must keep the original force trace and estimation choices available when interpreting a yank peak.

Abstract Reasoning

Start with the force carrier and time base. If \(\mathbf F(t)\) is a model, take its first time derivative where it exists.[1] If \(F_k\) is sampled data, state which component is measured, the sample interval and the numerical differentiation and filtering procedure, as the two published empirical studies do.[2][3] Then interpret a change-rate feature only against an independently established question: an event in a jump, or a time-lagged association with a neural signal.

This sequence gives two useful deductions. First, identical force levels can belong to different dynamic phases because their derivatives differ, while a high sustained force can have near-zero yank. Second, a finite-window rate of force development averages a change over its window rather than certifying a pointwise peak.[1] Shortening the interval changes both temporal detail and noise sensitivity. A claim about the event time or maximum rate is therefore conditional on the estimate's resolution and validation, not on the name alone.

The boundary test is equally important. If the input is a force trace, the derivative is yank regardless of whether a jump, grip or modeled muscle supplied the force. If the input is a non-force signal, the same calculus operation is a derivative but not this named physical metric. If the input is only one scalar force component, the result is component yank and cannot justify a statement about the complete force vector.

Knowledge Transfer

Sahrom and colleagues differentiate force-platform data from jumps; Jiang and colleagues differentiate dynamometer data from hand grasps.[2][3] The mathematical operation travels between them because both provide force as a function of time. What transfers is the typed computation and the force-level versus force-change distinction. What does not transfer automatically is a particular downstream interpretation: jump-event timing is not a claim about cortical-band activity, and a cortical correlation is not a universal event detector.

Derivative names the broader instantaneous-change operation. Yank fixes its input to force and its output to force change per unit time, while practical force measurements add specialist estimation boundaries. A metaphorical “yank” in a non-force domain would lose that identity.

Examples

Countermovement jump. Sahrom and colleagues recorded vertical ground-reaction force during human jumps and synchronized it with motion and muscle-activation measurements. They removed bodyweight to form the force trace, estimated its time derivative, then rectified and smoothed the result for selected event tests. Mapped back: the vertical force series supplies the force trajectory; numerical differentiation supplies an empirical component-yank estimate; rectification changes the component readout by discarding sign; motion and electromyography supply a separate check on the task-specific event interpretation. The authors note that the start of braking is not easily defined from yank alone, so the method does not replace every other event criterion.[2]

Sustained hand grasp. Jiang and colleagues measured grip force while four patients performed grasps through onset, hold and offset during intraoperative ECoG recording. They estimated the first time derivative of the scalar force trace and compared it with cortical-band time courses. Mapped back: grip force supplies the force trajectory; central differencing estimates the first time derivative; the result is a scalar readout that cannot establish unmeasured vector components; the analysis compares its timing with a separate neural signal as the task-specific interpretation. The reported high-frequency-band correlation with yank was stronger than with raw force at onset, but the analogous offset advantage was not statistically significant.[3] This is an observed association in four patients, not a causal law.

Structural Tensions

Transition sensitivity versus noise control. A derivative sharpens brief changes in force, the feature that made it useful for jump-event work.[2] Lin and colleagues warn that numerical differentiation can magnify electrical or mechanical noise, while Sahrom and colleagues filter their measured trace.[1][2] From those two facts, filtering more strongly can be expected to suppress false peaks but may blur or shift real rapid transitions; filtering less preserves detail but leaves a noisier estimate. Diagnostic: Does the chosen sampling and filtering preserve the event scale being claimed while suppressing noise-driven peaks? The exact mathematical derivative has no sensor-noise problem; the tension belongs to using yank as an empirical metric.

Structural–Framed Character

Yank sits toward the structural end of the structural–framed spectrum: changing from ground reaction to hand-grip force leaves the first time derivative of force as the same mathematical kind of quantity. The two studies supply different force recordings and aims, not new definitions.[2][3] Its definition is descriptive rather than evaluative, although choosing a yank threshold or using a peak to classify an event makes an applied judgment. The theoretical derivative does not depend on a human institution or instrument; empirical interpretation does depend on sampling, filtering, component selection and validation.

The name entered the literature through a biomechanics terminology proposal, and these jump and grasp studies show that it travels between unlike research tasks without establishing that it is standard throughout physics.[1][2][3] Such travel imports the already existing derivative operation into a force-specific use and recognizes the same force-change metric in each case; it does not transport a jump-specific event rule into a grasp task. Its character: a reusable formal metric near the structural end of the spectrum, with measurement-sensitive applications and no implied law of motor control.

Structural Core vs. Domain Accent

The core is a time derivative: an instantaneous rate of change obtained from a differentiable input. That mathematical structure is already broader than yank and belongs to Derivative. The domain accent is constitutive here because it fixes the input to force and the output to force change per unit time. Without force, a derivative remains but yank does not; without differentiation, a force history remains but no yank has been formed.

Biomechanical work adds recurring application constraints: component selection, noisy force sensors, finite sampling, rectification and validation against the event or signal under study.[1][2][3] These are not necessary for a theoretical yank value, yet they explain why a separately named metric is useful in the field. The transferable skeleton is the derivative operation; the force-typed reading and its measured-use limits justify this narrower entry.

Could a future Prime capture local change across non-force settings? That remains an open question: the broader idea would have to explain a recurring kind of change and support useful conclusions beyond the fact that a different quantity can also be differentiated. The jump and grasp cases show the narrower force-specific use.

Derivative supplies the limit-of-change operation that becomes yank when the changing function is force over time. Function Mapping describes the more general time-to-force assignment. Measurement matters when yank is estimated from a force sensor, but an instrument is not necessary for its mathematical identity.

Force is the quantity being differentiated, not a synonym for its derivative. A force value answers how much interaction is exerted at an instant; yank answers how that quantity is changing then.

Neighborhood in Abstraction Space

Yank (physics) sits in a sparse region of the domain-specific corpus (99th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2835 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-31

Not to Be Confused With

  • Force: ask whether the claim concerns \(\mathbf F(t)\) itself or its rate of change.[1]
  • Average rate of force development: ask whether the value spans a finite interval or is an instantaneous derivative. The former can estimate or average the latter under stated assumptions.[1]
  • Impulse: ask whether force was integrated over time rather than differentiated.
  • Jerk: ask whether acceleration was differentiated. Multiplying by mass gives yank only under a stated constant-mass force law.[1]
  • A rectified yank trace: ask whether negative component values were transformed to positive event-detection magnitudes, as in the jump study; such a trace no longer preserves the raw derivative sign.[2]
  • A biological mechanism: ask whether the evidence establishes a causal process or only reports an association with the force derivative, as in the hand-grasp study.[3]

References

[1] David C. Lin, Craig P. McGowan, Kyle P. Blum and Lena H. Ting, “Yank: the time derivative of force is an important biomechanical variable in sensorimotor systems,” Journal of Experimental Biology 222 (2019), jeb180414, DOI 10.1242/jeb.180414, https://bpb-us-w1.wpmucdn.com/sites.usc.edu/dist/1/927/files/2023/02/JEB-2019_Yank.pdf (published original Commentary, full PDF inspected; pp. 1–4 define the proposed name, vector derivative, interval-average RFD, conditional jerk relation and noise boundary). registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n ↩o ↩p ↩q ↩r ↩s ↩t

[2] Sofyan B. Sahrom, Jodie C. Wilkie, Kazunori Nosaka and Anthony J. Blazevich, “The use of yank-time signal as an alternative to identify kinematic events and define phases in human countermovement jumping,” Royal Society Open Science 7 (2020), 192093, DOI 10.1098/rsos.192093, https://upload.wikimedia.org/wikipedia/commons/b/b0/The_use_of_yank-time_signal_as_an_alternative_to_identify_kinematic_events_and_define_phases_in_human_countermovement_jumping.pdf (original open-access article, full PDF inspected; §§2.4, 3.2 and 4.1–4.3 describe force, processing and event limits). registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n ↩o ↩p ↩q ↩r ↩s

[3] Tianxiao Jiang et al., “Power Modulations of ECoG Alpha/Beta and Gamma Bands Correlate With Time-Derivative of Force During Hand Grasp,” Frontiers in Neuroscience 14 (2020), 100, DOI 10.3389/fnins.2020.00100, https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2020.00100/full (original research, full publisher HTML inspected; §§2.2, 2.7, 3.3 and 5 describe the four-patient task, yank estimate and onset/offset correlation limits). registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n ↩o ↩p