impulse

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

See also

• 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

Notes

Bibliography

• 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.

External links and references

• Dynamics