Impulse

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For other uses, see Impulse (disambiguation).

In classical mechanics, the impulse of a constant force is the product of the force and the time during which it acts. According to the Theorem of Impulse and Momentum (derived from Newton's second law), the impulse applied on a body is equal to the change in its linear momentum:

$\mathbf{F}\Delta t = m \Delta \mathbf{v}$

where

F is the constant total net force applied,

Δ t

is the time interval over which the force is applied,

m is the mass of the object,

Δv is the change in velocity produced by the force in the considered time interval,

FΔt is the impulse, and

mΔv = Δ(mv) is the change in linear momentum.

Impulse has the same units and dimensions as momentum (kg m/s or N·s = Huygens Hy)^{[citation needed]}.

The impulse of a time-varying force is calculated as the integral of force with respect to time:

$\mathbf{I} = \int \mathbf{F}\, dt$

where

I is impulse (sometimes marked J),

F is the force,

dt is an infinitesimal amount of time.

In the presence of a constant net force, impulse is equal to:

$\mathbf{I} = \mathbf{F}\Delta t$

Using the definition of force yields:

$\mathbf{I} = \int \frac{d\mathbf{p}}{dt}\, dt$

$\mathbf{I} = \int d\mathbf{p}$

$\mathbf{I} = \Delta \mathbf{p}$

In the technical sense, impulse is a physical quantity, not an event or force. However, the term "impulse" is also used to refer to a fast-acting force. This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, and is not physically possible. However, this is a useful model for certain purposes, such as computing the effects of ideal collisions, especially in game physics engines.

[edit] See also

specific impulse
Wave-particle duality defines an impulse for waves. The preservation of momentum at a collision is then called phase matching. Applications include:
- Compton effect
- nonlinear optics
- Acousto-optic modulator
- Umklapp scattering
- electron phonon scattering

[edit] References

Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers, 6th ed., Brooks/Cole. ISBN 0-534-40842-7.
Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics, 5th ed., W. H. Freeman. ISBN 0-7167-0809-4.