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	${\displaystyle {\mathsf {L}}{\mathsf {M}}{\mathsf {T}}^{-1}}$

Part of a series on
Classical mechanics
${\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}$ Second law of motion
History Timeline Textbooks
Branches Applied Celestial Continuum Dynamics Field theory Kinematics Kinetics Statics Statistical mechanics
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Koopman–von Neumann mechanics
Core topics Damping Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational frequency Angular acceleration / displacement / frequency / velocity
Scientists Kepler Galileo Huygens Newton Horrocks Halley Maupertuis Daniel Bernoulli Johann Bernoulli Euler d'Alembert Clairaut Lagrange Laplace Poisson Hamilton Jacobi Cauchy Routh Liouville Appell Gibbs Koopman von Neumann
Physics portal  Category
v t e

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: $${\displaystyle \sum \mathbf {F} \times \Delta t=\Delta \mathbf {p} .}$$^[1] 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).