1. Physics and Physical Measurement
Topic 1 Physical quantities and units

2. Learning outcomes
(a) show an understanding that all physical quantities consist of a numerical magnitude and a unit
(b) recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
(c) express derived units as products or quotients of the base units and use the named units listed in this syllabus as appropriate
(d) use base units to check the homogeneity of physical equations
(f) use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)
(g) make reasonable estimates of physical quantities included within the syllabus

3. For your notes All physical quantities have a magnitude and a unit
Base units are:
mass (kg)
length(m)
time (s)
current (A)
temperature (K)
amount of substance (mol)
Express derived units in terms of the base units
Use the SI units

4. Standards of Measurement
SI units are those of the Système International d’Unités adopted in 1960
Used for general measurement in most countries
Scientists and engineers need to make accurate measurements so that they can exchange information
To be useful a standard of measurement must be
Invariant, Accessible and Reproducible

5. Fundamental dimensions
There are seven fundamental dimensions.
A base unit is accurately defined for each quantity.
They are:
Length metre m
Mass kilogram kg
Time second s
Electric current ampere A
Thermodynamic temp Kelvin K
Amount of a substance mole mol
Luminous intensity candela Cd

6. Derived Quantities Speed, force , energy etc. are not base quantities.
Derived units allow us to measure any quantity.
Derived quantities are combinations of the fundamentals
e.g. speed
average speed = distance/time
So the derived unit is meters per second
We write derived units in the form ms-1 not m/s

7. Figuring out derived units
Write out an equation for the quantity you want to know the units of. ( The defining equation is best)
eg Pressure = F/A
Rewrite the equation substituting units for quantities
Eg [Pa]=[N] / [m2] or [N] [m-2]
Check if units are base units
m-2 
Repeat process for any none base units
F=ma [N] = [kg] [m] [s-2] all base units
So…….. [Pa]= [N] [m-2] = [kg] [m] [s-2] [m-2]
Simplified [Pa]= [kg] [s-2] [m-1]

8. Practise
Try these
Velocity
Density
Work
Power
Resistance

9. Writing Units two examples
A car has a velocity of 10ms-1
Notes
Do not use m/s
Meters and seconds are SI units
A metal has a density of 5Kgm-3
Kg not g is the SI unit
Per m3 is written m-3

10. Some Derived Units Acceleration ms-2 Angular acceleration rad s-2
Momentum kgms-1 or Ns
Others have specific names and symbols
Force kg ms-2 or N
Pressure kgm-1s-2or Pa
Resistance kgm2A-2s-3 or Ω
Of course there are so many things out there to measure there are many more.

11. Summary questions What are the base quantities?
What are the base units?
Give 5 derived units
What is a volume of 1m3 in cm3?
What is a pressure of 1Ncm-2 in Pa?
State 2 problems with this reading and rewrite it correctly:
Speed= 39 mph

12. Can you? State the fundamental units in the SI system.
Distinguish between fundamental and derived units
Give examples of derived units.
Convert between different units of quantities.
State units in the accepted SI format.