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impulse

 Definition/Summary Force = impulse per time: $\mathbf{F}\ =\ d\mathbf{I}/dt$. For constant force, impulse = force times time: $\mathbf{I}\ =\ \mathbf{F}\,\Delta t$ (by comparison, work done = force "dot" distance: $W\ =\ \mathbf{F}\cdot \Delta\mathbf{s}$). For varying force, impulse is the integral of force over time: $\mathbf{I}\ =\ \int\mathbf{F}\,dt$ (and work done is the integral of force over distance: $W\ =\ \int\mathbf{F}\cdot d\mathbf{s}$). Newton's second law (force = rate of change of momentum: $\mathbf{F}\ =\ d(m\mathbf{v})/dt$) integrated over time becomes: impulse = total change of momentum: $\mathbf{I}\ =\ \int d(m\mathbf{v})/dt\,dt\ =\ \int d(m\mathbf{v})\ =\ \Delta(m\mathbf{v})$. Impulse is a vector, with the same dimensions as momentum: $ML/T$, and is measured in units of newton seconds ($N.s\text{, or }kg\,m\,s^{-1}$).

 Equations $$\mathbf{F}\ =\ \frac{d\mathbf{I}}{dt}$$ $$\mathbf{I}\ =\ \int\mathbf{F}\,dt$$ Impulse-momentum theorem: $$\mathbf{I}\ =\ \int\frac{d(m\mathbf{v})}{dt}\,dt\ =\ \int d(m\mathbf{v})\ =\ \Delta(m\mathbf{v})$$

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 Breakdown Physics > Classical Mechanics >> Newtonian Dynamics