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:
where is the ultimate tensile strength of the material and 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.
A cascade of uranium centrifuges.
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™.
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.
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.
Most of the drag on an artillery shell comes from friction between the nose of the shell and the air, as the shell pushes air out of the way at very high speeds. But some of the drag on a shell comes from the sucking effect of the vacuum left behind the shell as it pushes air in front out of the way faster than air can move to fill the space left behind.
To combat this, many artillery shells employ a system called base bleed in which the shell produces gas at its rear to fill this vacuum. This gas produces very little thrust, but by reducing the effect of the vacuum it increases the range of the shell enormously, typically by around 30%. On the diagram on the right (taken from this patent) the top image shows a view from below, with the gas generator’s exhaust labelled “5”. The housing of the gas generator is labelled “1” and the casing of the shell “2”. The igniter that starts the gas generator is labelled “4” and the fuel charge that produces the gas is labelled “6”.
Many people assume that the terms “centre of mass” and “centre of gravity” are synonymous, but this is not the case.
Centre of mass is the point at which the distribution of mass is equal in all directions, and does not depend on gravitational field. Centre of gravity is the point at which the distribution of weight is equal in all directions, and does depend on gravitational field.
A toy bird balances when a pivot is placed at its centre of gravity.
The centre of mass and the centre of gravity of an object are in the same position if the gravitational field in which the object exists is uniform. In most cases this is true to a very good approximation: even at the top of Mount Everest (8848 metres) the gravitational field strength is still 99.6% of its standard value. You are unlikely ever to experience a difference between centre of mass and centre of gravity, as the gravitational field in which you find yourself is extremely uniform.
But if the gravitational field strength were greater towards your feet and weaker towards your head, then your centre of gravity would be below your centre of mass, perhaps somewhere around your knees. If the gravitational field strength were greater towards your head, and weaker towards your feet, then your centre of gravity would be above your centre of mass, perhaps somewhere around your shoulders.
The object on the left, in a uniform gravitational field, has overlapping centres of gravity and mass. For the object on the right, in which the gravitational field is stronger towards its base, the centre of gravity is below the centre of mass. Approaching a black hole the gradient of the gravitational field would be infinitely “steep”, leading to an incredible difference in gravitational field and death by spaghettification for anyone falling into a black hole.