How does impulse affect momentum?

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Answer 1 · 2015-07-29T14:04:30

Impulse is mathematically equal to the change in momentum which happens during the action of the impulsive force (the force causing impulse).

$\to F = \frac{d \to p}{d t}$ $vec F = (dvecp)/dt$

$\Rightarrow \to F d t = d \to p$ $implies vecFdt = dvecp$
Integrating both sides,

$\to F \int_{t_{0}}^{t} d t = \int_{p_{0}}^{p} d \to p$ $vecF int_(t""_0)^t dt = int_(p""_0)^p dvecp$

$\Rightarrow \to F (t - t_{0}) = \to p - \to p_{0}$ $implies vecF(t - t""_0) = vecp - vecp""_0$

By definition, impulse, $\to J = \to F (t - t_{0})$ $vecJ = vecF(t - t""_0)$

Thus, Impulse = Change in momentum