SI Units of Mechanics — Meters, Seconds, Kilograms

The SI Units of Mechanics are a specific subset of SI Units that are used in the physics of Mechanics — the study of forces, momentum, velocity, acceleration, mass and the like that describes the properties of physical objects.

In the introductory article on SI Units we covered the Base Quantities and Derived Quantities within science. We know that the seven base quantities are those from which all other quantities in science can be derived. These are:

1. Length
2. Mass
3. Time
4. Temperature
5. Luminous Intensity
6. Amount
7. Current

However, in classical mechanics, most of these simply are not relevant. It doesn’t matter how hot an object is, or how brightly it shines, or the sheer amount of material in the body, because these things do not effect its motion. Hence the subset of SI Units used in mechanics:

1. Length — Measured in meters
2. Mass — Measured in kilograms (kg)
3. Time — Measured in seconds (s)

MKS System

Mechanics is based only on the first three of these quantities, the MKS system. Or also the alternative metric CGS system (centimeter-gram-second) is also still in wide use, as it is more suitable for smaller objects. This covers the subjects of motions (mechanics), fluids, and waves, all pertinent physical quantities can be expressed in the units of length, mass, and time.

The Second

The second has a long history. It was once defined as 1/86,400 of a solar day. Which is where the length of the second, the minute, the hour, were originally derived from. (This determination is actually ancient, tracing all the way back to the Sumerians.)

However, we have improved upon our accuracy in the definition of a second (yet without actually changing its value) for the purpose of being able to measure it and keep it standard.

This has been found necessary for a number of reasons, but the most pressing being the simple fact that the period of the Earths rotation is not consistent enough — it does not always equal exactly 24 hours. Not only does the length of the day oscillate back and forth as it is, but the lengths of the day are also gradually growing longer.

Therefore, as a steady, consistent and measurable period readily found in nature, scientists have chosen to use Cesium atoms as the natural foundation upon which the second is now derived and measured.

They can be made to vibrate at a steady rate, and we also have the ability to detect and count these oscillations and so use them essentially as little clocks. So in 1967, the second was redefined as the time required for 9,192,631,770 — about 9.1 trillion — of these vibrations. (We can also write this in scientific notation as 9.192e9.)

In this way we arrive at an incredibly precise value for the second, without actually needing to change the general length of the second.

The Meter

The standard unit for length is the meter. Part of the metric system, from whence we can divide the meter in 100 to get centimeters, which we divide into 10 for mm, and so on. A base-10 system.

The meter was once defined in 1791 for the first time as the distance from the equator to the North Pole. In 1889 it was redefined as the distance between two engraved lines on a platinum-iridium bar now kept near Paris.

By 1960, it had become possible to define the meter even more accurately using the wavelengths of light, a very specific wavelength of light in fact, that of orange light emitted by krypton atoms.

Then again in 1983 the meter was revised again from whence we get its current definition, as the distance that light travels in a vacuum in 1/299,792,458th’s of a second. We arrived at this final definition once we found out that light travels exactly 299,792,458 m/s. As soon as we have a more accurate measurement, however, the meter will change slightly again.

Standard Mass

The standard unit of mass is the kilogram (kg). The kilogram is the only base unit of SI Units that is still defined by a physical artifact, which is known as the “International Prototype of the Standard Kilogram”. The rest have all been transferred and translated to being derived from universal, readily available, measurable quantities.

The physical object used as the standard for the kilogram is platinum-iridium cylinder created by George Matthey in 1879, that is now kept sage at the International Bureau of Weights and Measures near Paris. The cylinder is 39 mm tall, 39 mm in diameter, that weighs exactly 1kg. It is made of an alloy of 90% platinum and 10% iridium, and is stored at atmospheric pressure in a specially designed triple bell-jar in France.

Precise replicas of this standard kilogram were also kept at the U.S. National Institute of Standards and Technology (NIST) located in Maryland just outside of Washington, DC.

We are currently searching for other methods to measure the kilogram. Ones that are more accurate, more readily testable, which don’t rely on an well-guarded, old piece of metal. Yet as of today, every time you weigh anything, the kilograms (grams, micrograms, etc) that you read all trace back to platinum-iridium cylinder fashioned by George Matthey.

A Note On The Importance of Standardized Units

I can measure the distance from place to place on Earth in units based on the length of 1 of my strides. All odometers everywhere would read not kilometers, or miles, but “GSB” for “Great Strides of Brandon” which would be 1000 of my normal strides. Yet this is not practical, because what if someone else in the world has to measure the length of one single BS (“Brandon Stride”)? What if I was long dead, and so my exact stride length could no longer be accurately determined?

(This is actually a problem that we face now for calculating the ancient length of a stade.)

Therefore it has been becoming more and more relevant and practical to measure these base units as accurately as possible, and basing them on things which can always be measured by anyone, anywhere. They are also wanted to be measured with precision, because the algebraically derived units are only as precise as the base units they are derived from.