impulse, in mechanics: see momentum.

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


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
v = 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"


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



  • 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

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