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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 rac{d\mathbf{p}}{dt}\, dt
:\mathbf{I} = \int d\mathbf{p}
:\mathbf{I} = \Delta \mathbf{p}

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}

where
:F is the ''constant'' total net force applied,
:\Delta t is the time interval over which the force is applied,
m

v 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 Engine s.

Impulse has the same units and dimensions as momentum ( Kg M/s or N · S = Huygens Hy).


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