Editing Impulse (physics) (section)

{{short description|Integral of a comparatively larger force over a short time interval}}
{{Infobox physical quantity
|name = Impulse
|image = Armedforces jeffery tee shot.jpg
|caption = A large force applied for a very short duration, such as a golf shot, is often described as the club giving the ball an ''impulse''.
|unit = [[newton-second]] ([[Newton (unit)|N]]⋅[[second|s]])
|otherunits = [[kilogram|kg]]⋅[[metre|m]]/[[second|s]] in SI base units, [[pound (force)|lbf]]⋅[[second|s]]
|symbols = '''J''', '''Imp'''
|dimension = wikidata
|conserved = Yes
|derivations =
}}
{{Classical mechanics|cTopic=Fundamental concepts}}

In [[classical mechanics]], '''impulse''' (symbolized by {{math|'''J'''}} or '''Imp''') is the change in [[momentum]] of an object. If the initial momentum of an object is {{math|'''p'''<sub>1</sub>}}, and a subsequent momentum is {{math|'''p'''<sub>2</sub>}}, the object has received an impulse {{math|'''J'''}}:

<math display=block>\mathbf{J}=\mathbf{p}_2 - \mathbf{p}_1.</math>

[[Momentum]] is a [[Vector (physics)|vector]] quantity, so impulse is also a vector quantity: <math display="block">\sum \mathbf{F} \times \Delta t = \Delta \mathbf{p}.</math><ref>{{Cite book |title=Basic Physics: A Self-Teaching Guide |publisher=John Wiley & Sons |year=2020 |isbn=9781119629900 |pages=34 |language=en}}</ref> 
[[Newton’s second law of motion]] states that the rate of change of momentum of an object is equal to the resultant force {{mvar|F}} acting on the object:
<math display="block">\mathbf{F}=\frac{\mathbf{p}_2 - \mathbf{p}_1}{\Delta t},</math>

so the impulse {{mvar|J}} delivered by a steady [[force]] {{mvar|F}} acting for time {{math|Δ''t''}} is:
<math display="block">\mathbf{J}=\mathbf{F} \Delta t.</math>

The impulse delivered by a varying force acting from time {{mvar|a}} to {{mvar|b}} is the [[integral]] of the force {{mvar|F}} with respect to time:
<math display="block">\mathbf{J}= \int_a^b\mathbf{F} \, \mathrm{d}t.</math>

The [[International System of Units|SI]] unit of impulse is the [[newton second]] (N⋅s), and the [[dimensional analysis|dimensionally equivalent]] unit of momentum is the kilogram metre per second (kg⋅m/s). The corresponding [[English engineering unit]] is the [[pound (force)|pound]]-second (lbf⋅s), and in the [[British Gravitational System]], the unit is the [[Slug (unit)|slug]]-foot per second (slug⋅ft/s).