Starting from , we can re-arrange the terms to get

where *F* could represent either a constant force or the average force for the duration Δ*t*.

The quantity is given the name **impulse**. It is usually denoted by the symbol *J* and has the unit N s.

The following equation is called the impulse-momentum theorem.

Quite simply, it says that the application of a force *F* (constant or average) for a duration of time causes a momentum change of .

For example, to increase a mass’s momentum from 0 kg m s^{-1} to 12 kg m s^{-1} requires an impulse of 12 N s. This impulse can be delivered by exerting a force of 1 N for 12 s on the mass, or 2 N for 6 s, or 3 N for 4 s, or 8 N for 1.5 s,… because all of them correspond to an impulse of 12 N s.

*Buying time to reduce impact force*

The concept of impulse is very helpful in understanding why gymnasts always bend their knees when they land. To come to a rest, a gymnast must lose all the downward momentum. This requires an upward impulse. Whether the bent knees are bent or straight, the required momentum change (and thus the required impulse) during the landing is the same. By bending the knees, however, gymnasts extend the duration of impact Δ*t*. This allows them to achieve the landing with a smaller impact force *F*. In short, the required is the same. But small *F* big Δ*t* is a graceful touch-down whereas big *F* small Δ*t* is a bone-shattering experience.

The same physics applies for anti-crush devices such as air bags, car crumple zones, safety nets, stuntman boxes, corrugated paper, bubble wraps. The required impulse *J* is fixed, so it is always about extending the impact duration Δ*t* to reduce the impact force *F*.

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**Demonstrations**

Bird Egg

Gymnasts and Air Bags

**Concept Test**

0441

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