Mks Units

The first principle of any exact physical science is measurement. In Newtonian dynamics, there are three fundamental quantities that are subject to measurement:

1. Intervals in space; that is, length.
2. Quantities of inertia, or inertial mass, possessed by various bodies.
3. Intervals in time.

Any other type of measurement in Newtonian dynamics can (effectively) be reduced to some combination of measurements of these three quantities.

Each of the three fundamental quantities—length, mass, and time—is measured with respect to some convenient standard. The system of units currently used by most scientists and engineers is called the mks system—after the first initials of the names of the units of length, mass, and time, respectively, in this system. That is, the meter, the kilogram, and the second.

The mks unit of length is the meter (symbol m). The meter was formerly the distance between two scratches on a platinum-iridium alloy bar kept at the International Bureau of Weights and Measures in Sèvres, France, but is now defined as the distance travelled by light in vacuum in 1/299 792 458 seconds.

The mks unit of mass is the kilogram (symbol kg). The kilogram was formally defined as the mass of a platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures in Sèvres, France, but is now defined in such a manner as to make Planck's constant take the value $6.626\,070\,15\times 10^{-34}$ when expressed in mks units.

The mks unit of time is the second (symbol s). The second was formerly defined in terms of the Earth's rotation, but is now defined as the time required for 9 192 631 770 complete oscillations associated with the transition between the two hyperfine levels of the ground state of the isotope Cesium 133.

In addition to the three fundamental quantities, Newtonian dynamics also deals with derived quantities, such as velocity, acceleration, momentum, angular momentum, et cetera. Each of these derived quantities can be reduced to some particular combination of length, mass, and time. The mks units of these derived quantities are, therefore, the corresponding combinations of the mks units of length, mass, and time. For instance, a velocity can be reduced to a length divided by a time. Hence, the mks units of velocity are meters per second:

$$[v] = \frac{[L]}{[T]} = {\rm m\,s^{-1}}.$$ (1.1)

Here, $v$ stands for a velocity, $L$ for a length, and $T$ for a time, whereas the operator $[\cdots]$ represents the units, or dimensions, of the quantity contained within the brackets. Momentum can be reduced to a mass multiplied by a velocity. Hence, the mks units of momentum are kilogram-meters per second:

$$[p] = [M][v] = \frac{[M][L]}{[T]} = {\rm kg\,m\,s^{-1}}.$$ (1.2)

Here, $p$ stands for a momentum, and $M$ for a mass. In this manner, the mks units of all derived quantities appearing in Newtonian dynamics can easily be obtained.

Some combinations of meters, kilograms, and seconds occur so often in physics that they have been given special nicknames. Such combinations include the newton, which is the mks unit of force, and the joule, which is the mks unit of energy. These so-called derived units are listed in Table 1.1.

Table 1.1: Derived units.

Physical Quantity	Derived Unit	Abbreviation	Mks Equivalent
Force	newton	N	${\rm m\,kg\,s}^{-2}$
Energy	joule	J	${\rm m^{2}\,kg\,s}^{-2}$
Power	watt	W	${\rm m^{2}\,kg\,s}^{-3}$
Pressure	pascal	Pa	${\rm m^{-1}\,kg\,s}^{-2}$