Topic 1 – Physical Measurements

1.2a – The SI Units

The Fundamental Units

The SI system uses just 7 fundamental units.

All other units can be derived from these 7.

These fundamental units were originally based on standard definitions.

The metre (quantity length [L] symbol m) – originally defined by two marks scored on a platinum-iridium bar stored in a vault in Paris. Now defined in terms of the distance travelled by light in a vacuum in a known time.

The Fundamental UnitsThe kilogram (quantity mass [M], symbol kg) – currently

defined by reference to a platinum-iridium standard kilogram held in a vault in Paris.

The second (quantity time [T], symbol s) – originally defined as 1/86400 of a mean solar day it is now defined as 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.

The Fundamental UnitsThe Ampere (quantity current [C], symbol A) – defined

as that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in a vacuum, would produce between these conductors a force equal to 2 x 10-7 Nm-1 of length.

The kelvin (quantity Temperature [t], symbol K) – defined as being 1/273.16 of the triple point of pure water.A Celcius temperature is calculated using

/ Co =T /K−273.15

The Fundamental UnitsThe mole (quantity amount of substance [N], symbol

mol) – defined as being the amount of substance which contains as many elementary entities as there are atoms in 0.012 kg of carbon-12.This number is known as Avagadro's number (N

A) and is

6.022x1023 mol-1

The candela (quantity luminous intensity [I], symbol cd) – defined as 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.

All other units are derived from these fundamental units.

Example: express the Newton in terms of fundamental units.

Newton is the unit of force

Force = mass x acceleration (amongst others)

[N] = [kg] x [ms-2]

N = kgms-2

Derived units

Derived Units

State the following quantities in terms of fundamental units.

Energy

Concentration

Frequency

Power

Pressure

Electric Charge

Voltage

SI Weirdness

When writing SI units:

Always use negative indices and not “/”

When writing units in table headings and graph axes use /kg and not (kg) / means has been divided by the unit which is technically

correct.

In general write the most positive index first. m2kgA-1s-3 for the Volt

SI Prefixes

Instead of writing units in scientific notation physicists often use prefixes in front of the units instead.

This makes it easier to read values in reports etc.

In general use scientific notation in results tables and intermediate work (as this makes working with large numbers much easier) and use prefixes for the final answer.

SI Prefixes

Name Symbol Exponent Multiplier

Peta P 1015 1 000 000 000 000 000

Tera T 1012 1 000 000 000 000

Giga G 109 1 000 000 000

Mega M 106 1 000 000

Kilo k 103 1 000

100 1

milli m 10-3 0.001

micro μ 10-6 0.000 001

nano n 10-9 0.000 000 001

pico p 10-12 0.000 000 000 001

femto f 10-15 0.000 000 000 000 001

SI Prefixes

Express each of the following quantities in both Scientific notation and using prefixes

27.647J

150 564 kL

0.003 672 nF

178.3671 μC

258 245 mK