Impulse (physics)
| Impulse | |
|---|---|
|
Common symbols
|
J, Imp |
| SI unit | Newton second (N · s) |
|
Other units
|
pound · s |
| SI dimension | momentum |
| Conserved? | yes |
In classical mechanics, impulse (symbolized by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction. The SI unit of impulse is the newton second (N·s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg·m/s). The corresponding English engineering units are the pound-second (lbf·s) and the slug-foot per second (slug·ft/s).
A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time therefore produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly.
The impulse is the integral of the resultant force (F) with respect to time:
Impulse J produced from time t1 to t2 is defined to be
where F is the resultant force applied from t1 to t2.
From Newton's second law, force is related to momentum p by
Therefore,
where Δp is the change in linear momentum from time t1 to t2. This is often called the impulse-momentum theorem.
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