Impulse

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Categories: Physical quantity | Classical mechanics

For other uses, see Impulse (disambiguation).

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

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{I} = \int \mathbf{F}\, dt

where

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:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{I} = \int \frac{d\mathbf{p}}{dt}\, dt

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{I} = \int d\mathbf{p}

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{I} = \Delta \mathbf{p}

This is often called the impulse-momentum theorem.^[1]

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:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{I} = \mathbf{F}\Delta t = m \Delta \mathbf{v} = \Delta\ p

where

F is the constant total net force applied,

Failed to parse (Missing texvc executable; please see math/README to configure.): \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).

1 See also
2 Notes
3 Bibliography
4 External links and references

Notes

^ See, for example, section 9.2, page 257, of Serway (2004).

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.