Where does impulse collide?

The effect of a force acting over an interval of time, defined as the force integrated across that interval, which equals the change in an object's momentum: this is the impulse-momentum theorem, a direct restatement of Newton's second law. Kleppner and Kolenkow's An Introduction to Mechanics (2010) develops it as the time-integral counterpart to work, and it explains why a short, hard hit and a long, gentle push can produce the same change in motion. The referent here is a physical quantity with units of force times time, and it has nothing to do with a person acting on a sudden urge, a system's response to a spike, or an unplanned purchase.[1]

Unit

One force acting over one time interval, in newton-seconds (kg m/s)

Recovery means

Not applicable

Measured by

Computed as the integral of measured force over time, or read off as the resulting change in momentum

A disposition to act quickly on urges with little planning or regard for consequences, treated as a stable trait that varies across people: the standard instrument is the Barratt Impulsiveness Scale, whose current form Patton, Stanford, and Barratt (1995) factored into attentional, motor, and non-planning components. The referent is a psychological tendency of a person, scored from self-report items, and it is measured in points on a questionnaire rather than in units of force. It is unrelated to the physical quantity of force times time, to a system's response to a spike, or to a specific act of buying.[2]

Unit

One person's standing on a trait, scored as a questionnaire total

Recovery means

Not applicable

Measured by

Assessed by self-report scales such as the Barratt Impulsiveness Scale and by behavioural tasks of response inhibition

The output that a linear, time-invariant system produces when its input is a single unit impulse, a spike of unit area concentrated at one instant: because such a system is fully characterised by this one output, its response to any input can be recovered by convolving that input with the impulse response. Oppenheim, Willsky, and Nawab's Signals and Systems (1997) makes this the central tool for analysing filters and circuits. The referent is a function that describes an engineered or physical system, not a bodily force, not a personality trait, and not a shopping decision.[3]

Unit

One system's output to a unit impulse, a function of time

Recovery means

Not applicable

Measured by

Obtained by exciting the system with an impulse (or estimating it from measured input and output) and recording the output waveform