# How Fast Can You Spin?

Imagine you have a cylinder, of any dimensions (i.e. it can be flat like a CD, or tall like a drink can). How fast can you possibly rotate that cylinder?

When an object is spun, the centrifugal forces in its rotating reference frame try to pull it apart. It turns out that the maximum speed that the outside edge of a cylinder can rotate at is given by:

$v_{max} = \sqrt{\frac{\sigma}{\rho}}$

where $\sigma$ is the ultimate tensile strength of the material and $\rho$ is the material’s density.

The largest value for metals is that of maraging steels, whose production and distribution is carefully monitored, as it can be used in fast-rotating uranium enrichment centrifuges. (It is also used in the construction of golf clubs and some specialist bicycles.) These centrifuges spin at speeds up to 1500 revolutions per second (90 000 revolutions per minute) and are therefore right on the edge of the capability of the steel to hold itself together.

You would be forgiven for thinking that metals would score best in this particular test, but even the strongest metals are easily beaten into submission by crystals and carefully crafted polymers like Vectran™Kevlar™, and Zylon™.

# Breaking length

Breaking length (also called self-support length) is a way of measuring the strength of a material; it is the maximum length of a column of a material that can support its own weight if it is anchored only at the top. For example, the breaking length of concrete is 0.44 kilometres, which means that if you constructed a 440-metre long column of concrete you could hang it from its top and it would support its own weight, but a 441-metre long column would break.

As you might expect, the top end of the list is dominated by materials that have been specially engineered for strength:

• Zylon is used in the manufacture of tennis racquets, seat belts and even the Spirit and Opportunity Mars rovers.
• Dyneema, made of ultra-high-molecular-weight polyethylene fibres, is used in body armour, bow strings and climbing equipment
• Kevlar is famously used in body armour, but is also used in racing boat sails and motorcycle safety clothing.
• Carbon Fibre, when used to reinforce polymers, is used in Formula One cars, boat hulls and bicycle frames.