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Common symbol(s):| I, J|
SI unit:| N · s = kg · m/s|
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In classical mechanics, impulse (noted as I or J) is defined as the integral of a force with respect to time. When a force is applied to a rigid body it changes the momentum of that body. If the momentum of an object changes, then either the mass or the velocity or both change. If the mass remains unchanged, as is most often the case, then the velocity changes and acceleration occurs. A force produces an acceleration, and the greater the force acting on an object, the greater its change in velocity and, hence, the greater its change in momentum. However, the change in momentum also depends on the duration of the force. The quantity of impulse is force × time interval, or in shorthand notation:
A force applied over a long time produces more change in momentum than does the same force applied briefly. A small force applied for a long time can produce the same change in momentum as a large force applied briefly, because momentum is the product of force and time. The SI unit of impulse is thenewton second (Ns). Contents [hide] * 1 Mathematical derivation in the case of an object of constant mass * 2 Variable mass * 3 See also * 4 Notes * 5 Bibliography * 6 External links| -------------------------------------------------
Mathematical derivation in the case of an object of constant mass Impulse J produced from time t1 to t2 is defined to be
where F is the force applied from t1 to t2.
From Newton's second law, force is related to momentum p by
where Δp is the change in momentum from time t1 to t2. This is often called the...