Physics Study Guide/Basic Units

The SI System of Measurement

Fundamental units

These are basic units upon which most units depends.

Time

Time is defined as the duration between two events. In the international system of measurement (S.I.) the second (s) is the basic unit of time and it is defined as the time it takes a cesium (Cs) atom to perform 9,192,631,770 complete oscillations. The Earth revolves around its own axis in 86400 seconds with respect to the Sun; this is known as the mean solar day, and the 86400th part of one day is known as a second.

Length

In the international system of measurement (S.I.) the metre (m) ('meter' in the US) is the basic unit of length and is defined as the distance travelled by light in a vacuum in 1/299,792,458 second. This definition establishes that the speed of light in a vacuum is precisely 299,792,458 metres per second.

Mass

In the international system of measurement (S.I.) the kilogram (kg) is the basic unit of mass and is defined as the mass of a specific platinum-iridium alloy cylinder kept at the Bureau International des Poids et Mesures in Sèvres, France. A duplicate of the Sèvres cylinder is kept at the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland. See Wikipedia article.

Current

In the international system of measurement (S.I.) the ampere (A) is the basic measure of electrical current. It is defined as the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre (m) apart in vacuum, would produce between these conductors a force equal to 2×10^-7 newton (N) per metre of length.

Unit of Thermodynamic Temperature

The kelvin (K), unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Unit of Amount of Substance

1. The mole (mol) is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilograms (12 grams) of carbon 12.

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Luminous Intensity

The candela (cd) is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. (A steradian (sr) is the SI unit of solid angle, equal to the angle at the centre of a sphere subtended by a part of the surface equal in area to the square of the radius.)

Derived Units

These are units obtained by combining two or more fundamental units.

Charge

The SI unit of charge is the coulomb (C). It is equal to ampere times second: $1\ \mathrm {C} =1\ \mathrm {A} \cdot \mathrm {s}$

Velocity

The SI unit for velocity is in m/s or metres per second.

Force

The SI unit of force is the newton ($N$), named after Sir Isaac Newton. It is equal to $1\ \mathrm {kg} \cdot \mathrm {m} /\mathrm {s} ^{2}$.

Energy

The SI unit of energy is the joule (J). The joule has base units of kg·m²/s² = N·m. A joule is defined as the work done or energy required to exert a force of one newton for a distance of one metre. See Wikipedia article.

Pressure

The SI unit of pressure is the pascal (Pa). The pascal has base units of $\mathrm {N} /\mathrm {m} ^{2}$ or $\mathrm {kg} /\mathrm {m} \cdot \mathrm {s} ^{2}$. See Wikipedia article.

Prefixes

Prefix	yotta	zetta	exa	peta	tera	giga	mega	kilo	hecto	deca		deci	centi	milli	micro	nano	pico	femto	atto	zepto	yocto
Symbol	Y	Z	E	P	T	G	M	k	h	da		d	c	m	µ	n	p	f	a	z	y
10n	1024	1021	1018	1015	1012	109	106	103	102	101	100	10-1	10-2	10-3	10-6	10-9	10-12	10-15	10-18	10-21	10-24
1000n	10008	10007	10006	10005	10004	10003	10002	10001						1000-1	1000-2	1000-3	1000-4	1000-5	1000-6	1000-7	1000-8

Astronomical Measurements

The SI units are not always convenient to use, even with the larger (and smaller) prefixes. For astronomy, the following units are prevalent:

Julian Year

The Julian year is defined by the IAU as exactly 365.25 days, a day being exactly 60*60*24 = 86,400 SI seconds. The Julian year is therefore equal to 31,557,600 seconds.

Astronomical Unit

The Astronomical Unit (au or ua), often used for measuring distances in the Solar system, is the average distance from the Earth to the Sun. In 2012 this was defined as exactly 149,597,870,700 metres. Previously it was 149,597,870,691 m, ± 30 m.

Light Year

The light year (ly) is defined as the distance light travels in a homogeneous isotopic non-attenuating medium (a vacuum) in one Julian year. Due to the word "year", the light year is often mistaken for a unit of time in popular culture. It is, however, a unit of length (distance), and is equal to exactly 9,460,730,472,580,800 m.

Parsec

The parsec (pc), or "parallax second", is the distance of an object that appears to move two arc-seconds against the background stars as the Earth moves around the sun, or by definition one arc-second of parallax angle. This angle is measured in reference to a line connecting the object and the Sun, and thus the apparent motion is one arc-second on either side of this "central" position. The parsec is approximately 3.26156 ly.