Impulse (physics)

Impulse
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.
Common symbols	J, Imp
SI unit	newton-second (N⋅s)
Other units	kg⋅m/s in SI base units, lbf⋅s
Conserved?	Yes
Dimension	${\displaystyle {\mathsf {L}}{\mathsf {M}}{\mathsf {T}}^{-1}}$

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Classical mechanics
${\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}$ Second law of motion
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In classical mechanics, impulse (symbolized by J or Imp) is the change in momentum of an object. If the initial momentum of an object is p₁, and a subsequent momentum is p₂, the object has received an impulse J:

$${\displaystyle \mathbf {J} =\mathbf {p} _{2}-\mathbf {p} _{1}.}$$

Momentum is a vector quantity, so impulse is also a vector quantity: $${\displaystyle \sum \mathbf {F} \times \Delta t=\Delta \mathbf {p} .}$$ Newton’s second law of motion states that the rate of change of momentum of an object is equal to the resultant force F acting on the object: $${\displaystyle \mathbf {F} ={\frac {\mathbf {p} _{2}-\mathbf {p} _{1}}{\Delta t}},}$$

so the impulse J delivered by a steady force F acting for time Δt is: $${\displaystyle \mathbf {J} =\mathbf {F} \Delta t.}$$

The impulse delivered by a varying force acting from time a to b is the integral of the force F with respect to time: $${\displaystyle \mathbf {J} =\int _{a}^{b}\mathbf {F} \,\mathrm {d} t.}$$

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