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impulse, in mechanics: see momentum.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

In classical mechanics, an impulse is defined as the integral of a force with respect to time:

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

- I is impulse (sometimes marked J),

- F is the force, and

- dt is an infinitesimal amount of time.

A simple derivation using Newton's second law yields:

- $mathbf\{I\}\; =\; int\; frac\{dmathbf\{p\}\}\{dt\},\; dt$

- $mathbf\{I\}\; =\; int\; dmathbf\{p\}$

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

- p is momentum

This is often called the impulse-momentum theorem.

As a result, an impulse may also be regarded as the change in momentum of an object to which a force is applied. The impulse may be expressed in a simpler form when both the force and the mass are constant:

- $mathbf\{I\}\; =\; mathbf\{F\}Delta\; t\; =\; m\; Delta\; mathbf\{v\}\; =\; Delta\; p$

where

- F is the constant total net force applied,

- $Delta\; t$ is the time interval over which the force is applied,

- m is the constant mass of the object,

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

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

However, it is often the case that one or both of these two quantities vary.

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.

Impulse has the same units and dimensions as momentum (kg m/s = N·s).

Using basic math, Impulse can be calculated using the equation:

$mathbf\{F\}t\; =\; Delta\; p$

$Delta\; p$ can be calculated, if initial and final velocities are known, by using "mv(f) - mv(i)" or otherwise known as "mv - mu"

where

- F is the constant total net force applied,

- $t$ is the time interval over which the force is applied,

- m is the constant mass of the object,

- v is the final velocity of the object at the end of the time interval, and

- u is the initial velocity of the object when the time interval begins.

Hence: $mathbf\{F\}t\; =\; mv\; -\; mu$

- Specific impulse
- Momentum
- 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

- 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.

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Last updated on Monday September 22, 2008 at 06:57:27 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday September 22, 2008 at 06:57:27 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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