Impulse

The impulse of a constant force is the product of the force and the time during which it acts:

Key formula

$\vv{I} = \vv{F}\,\Delta t$

Impulse is what transfers momentum from one body to another, just as work transfers energy. It is a vector, directed like the force, and is measured in $\text{N}\cdot\text{s}$ (equivalent to $\text{kg}\cdot\text{m/s}$, the same units as $\vv{p}$: this is no coincidence).

The useful intuition is that the same change in momentum can be obtained in many ways: a large force for a short time, or a small force for a long time, provided the product $\vv{F}\,\Delta t$ is the same. This is the principle behind mattresses, airbags, boxing gloves and deformable bumpers: by lengthening $\Delta t$ you reduce the maximum force $F = \Delta p/\Delta t$ for the same change in momentum.

When the force is not constant, the impulse is the area under the graph $F(t)$; the formula $\vv{I} = \vv{F}\,\Delta t$ then holds with $\vv{F}$ taken to mean the average force over the interval.

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Topics: Momentum and collisions Concepts: Impulse · Momentum

Related exercises: Crash test with airbag · Three balls against the wall · Why airbags save lives