Impulse

Impulse

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Impulse

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

\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:

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

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

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

where

p is momentum

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:

\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,

?v is the change in velocity produced by the force in the considered time interval, and

m?v = ?(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