# Why do safety helmets have a softer inner layer nearer the head?

I know that when an object collides onto the helmet, it causes an inelastic collision so that energy is absorbed by the structure of the helmet, so what exactly does the softer inner layer do? Does it prevent the energy from being transferred into the head?

• What about comfort? – Bernhard Aug 12 '14 at 5:40

## 1 Answer

While people normally quote Newton's Second law as $\vec F = m \vec a$, it is better written as $$\vec F = \frac{d\vec p}{dt}$$ Force is a rate of change in momentum. This means that the average force applied when an object undergoes some discrete change in its momentum is $$F_{\text{avg}} = \frac{\Delta p }{\Delta t}$$ The change in your momentum divided by the time it takes to effect that change.

If you are going to get into a crash, there is little we can do about the $\Delta p$ term; Your head is going to have to stop, no matter what. But if we can, by putting in a soft material, increase the $\Delta t$ term, there will be a lower average force on your head.