1.1 – Measurements in physics
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| https://physics.nist.gov/cuu/Units/units.html |
Quantities and units
Fundamental quantities are those quantities that are considered to be so basic that all other quantities need to be expressed in terms of them. In the density equation ρ = m/V only mass is chosen to be fundamental (volume being the product of three lengths), density and volume are said to be derived quantities.
Note that the symbols in the equation are all written in italic (sloping) fonts – this is how we can be sure that the symbols represent quantities. Units are always written in Roman (upright) font because they sometimes share the same symbol with a quantity. So “m” represents the quantity “mass”
but “m” represents the unit “metre”. We will use this convention throughout the IB course.
In SI (Système international d’unités) there are seven fundamental units and only six of these will use on the Diploma course (the seventh, the candela, is included for completeness). The fundamental quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. The units for these quantities have exact definitions and are precisely reproducible, given the right equipment. This means that any quantity can, in theory, be compared with the fundamental measurement to ensure that a measurement of that quantity is accurate. In practice, most measurements are made against more easily achieved standards so, for example, length will usually be compared with a standard metre rather than the distance travelled by light in a vacuum. They are:
metre (m): the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second.
kilogram (kg): mass equal to the mass of the international prototype of the kilogram kept at the Bureau International des Poids et Mesures at Sèvres, near Paris.
second (s): the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
ampere (A): that constant current which, if maintained in two straight parallel conductors of infinite length, negligible circular cross-section, and placed 1 m apart in vacuum, would produce between
these conductors a force equal to 2 × 10^–7 newtons per metre of length.
kelvin (K): the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
mole (mol): the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon–12. 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.
candela (cd): the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10^12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
All quantities that are not fundamental are known as derived and these can always be expressed in terms of the fundamental quantities through a relevant equation.
The units used for fundamental quantities are unsurprisingly known as fundamental units and those for derived quantities are known as derived units. It is a straightforward approach to be able to express the unit of any quantity in terms of its fundamental units, provided you know the equation relating the quantities. Nineteen fundamental quantities have their own unit but it is also valid, if cumbersome, to express this in terms of fundamental units. For example, the SI unit of pressure is the pascal (Pa), which is expressed in fundamental units as m^−1 kg s^−2.
Notice that when we write the unit newton in full, we use a lower case n but we use a capital N for the symbol for the unit – unfortunately some word processors have default setting to correct this so take care! All units written in full should start with a lower case letter, but those that have been derived in honour of a scientist will have a symbol that is a capital letter. In this way there is no confusion between the scientist and the unit: “Newton” refers to Sir Isaac Newton but “newton” means the unit. Sometimes units are abbreviations of the scientist’s surname, so amp (which is a shortened form of ampère anyway) is named after Ampère, the volt after Volta, the farad, Faraday, etc.
The unit of force is the newton (N). This is a derived unit and can be expressed in terms of fundamental units as kg m s^−2. The reason for this is that force can be defined as being the product of mass and acceleration or F = ma. Mass is a fundamental quantity but acceleration is not. This is such a common unit that it has its own name, the newton, (N ≡ kg m s^−2 – a mathematical way of expressing that the two units are identical). So if you are in an examination and forget the unit of force you could always write kg m s^−2 (if you have time to work it out!).
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