# 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™.

# Rectangles and Squares

Just very quickly, to clarify:

• A rectangle is any two-dimensional shape with four right-angled corners.
• A square is a rectangle in which all four sides are the same length.
• Therefore all squares are rectangles, but not all rectangles are squares.

I hope that clears things up.

# Change in Day Length with Latitude

As the Earth moves around the Sun, the length of the day (defined as the time between sunrise and sunset) changes. The extent to which it changes depends on latitude, as shown in the graph below:

As you can see, the length of a day changes far more during the year at higher latitudes than at lower latitudes. (Latitudes beyond 66°33′ are not shown because the Sun does not always rise or set at these latitudes.) The graph runs from one winter solstice to the next, with the two equinoxes clearly visible in March and September.

It’s quite interesting to look at by how much the length of a day changes every day. This graph would have the same shape as the previous one, but not if we look at percentage change. In a way, this gives an impression of how quickly it appears that “the nights are drawing in”.

At higher latitudes the length of day changes quite noticeably in early January and mid-November.  In some situations two adjacent days are different in length by nearly five minutes, and at some points the day loses nearly fourty minutes over the course of a single week.