1. 2.1.1-2 Physical quantities and SI units

2. Introduction to Base Quantities and Units
Before we start:
What is 33? What is 32? What is 31? What is 30?
What is 3-1? What is 3-2?
What does m/s mean?
What does m/s2 mean?
So from now on you should write ms-1 and ms-2 etc. because it is more professional.
We also subtract numbers rather than minusing them and Multiply instead of timesing etc

3. Sort the following abbreviations and words into two columns which show which are quantities and which are units - you might want to do this in pencil!
m, m2, mass, length, kg, force, N, velocity, time, s, area,ms-1
Quantities
Length
Force
Time
Mass
Area
Velocity
Units m N s Kg m2
ms-1

4. These are the units that correspond to the base quantities.
A base quantity is one that is defined without reference to any other quantities.
All other quantities are derived from these ones. We need to know about 6 of the 7.
For example, Area is “made” from length x length so it is not fundamental.
Length is more basic and is therefore a Base quantity
Base Units
These are the units that correspond to the base quantities.

5. Base Quantities and Units
You must learn the following base units and quantities:
Base Quantity Base Unit
mass (m) kilogram (kg)
time (t) second (s)
length (l) metre (m)
electric current (I) ampere (A)
temperature (T,) kelvin (K)
amount of substance (n) mole (mol)
{luminous Intensity candela (cd) }
You might like to try and find definitions for these quantities

6. or MLT-2 - note the use of capitals.
What are the base units of newton?
We are looking at force (measured in newton) so use F=ma.
The base units will be the same as those of mass x acceleration
kg ms-2
What are the base quantities of force?
The same as the base quantities of kgms-2
ie mass x length x time-2
or MLT-2 - note the use of capitals.

7. What are the base units of work?
Remember work = force x distance
giving kgms-2 x m = kgm2s-2
and the base quantities will be ML2T-2
What are the base units of energy? Use Ek =1/2 mv2.
You should get the same answer - as you should have expected.
Why?

8.  Prefix Symbol Multiplier pico p 10-12 nano n 10-9 micro 10-6 milli m
Prefixes
In order to make our life simpler a set of prefixes have been developed. These need to be learned and understood.
Prefix
Symbol
Multiplier
pico p
10-12
nano n
10-9
micro 
10-6
milli m
10-3
kilo k
10 3
mega M
10 6
giga G
10 9

9. Length m Mass g Time s Current A K Amount of substance mol Temperature
pico
10-12
 of a  ray
1012 protons
Molecular spin period
6*106 e- per second
Not poss
1010 units
nano
10-9
Olive oil mol.
Dust speck
Computer switch time
Ionn current match flame
Amount of C in a full stop
micro
10-6
Size of bactria
Sand grain
Period of radio wave
Current in digital watch
As low as we can go
Salt grain
milli
10-3
Diam. of pin head
Drop of rain
Period of sound wave
1.5K res & 1.5V cell
CO2 in a breath
Ref.
unit
Height of desk
Door mouse
Tick of a clock
I in a car light
Temp in space
2g of H gas
kilo
103
2.5 laps of track
1 litre water
neutron
lifetime
“Chunnel” train I
MP of Silver
Bucket of H2O
mega
106
"End to End”
1 m3 water
11 days
Houses in lg town
Atmosphere of Sun
Water you use in a year
giga
109
Diameter of Sun
Giant tree
30 years
All towns in GB
Core of v. hot star
O2 inhaled in life

10. Physics Factsheet 08

11. Homogeneity of Equations
For an equation to be true, the units and physical quantities must be homogeneous.
e.g. look at v2 = u2 +2as
you might already know that this equation is correct!
look at the base units of each element of the equation.
v2  (ms-1)2 = m2s-2
u2  (ms-1)2 = m2s-2
2ax  ms-2 m = m2s-2
They are the same in each element so the equation is homogeneous in terms of units. If this is so, it will also be homogeneous in terms of quantities.

12. Worksheet – Using SI Units Stretch and Challenge – Homogeneity (2)

13. r
Area = A
For a circle A = r2
Can you see that  can’t have any units as the two sides are homogeneous.
We could write A = r2.
In terms of quantities and units it would be correct
BUT the formula would not be correct.

14. Now do the same with s = ut + at2.
Is it homogeneous in terms of units?
The answer is yes but you should know that the equation is wrong!
It is not sufficient for an equation to be homogeneous for it to be correct.

15. If any of the equations that we have used here are not familiar to you, or have taken some remembering start learning them now!
Use your text book, notes and syllabus formula booklet.
It is much better to know them and understand them than trying to work out which one to use.

16. Presentation of Data in tables
Table headings
It is expected that all table column (or row) headings will consist of a quantity and a unit.
The quantity may be represented by a symbol or written in words. There must be some kind of distinguishing notation between the quantity and the unit.
Quantities should be represented
with a symbol in italics, while units are upright. For example:
T / °C T (°C) T in °C
are all acceptable as column headings.
Remember to avoid notations that do not distinguish between the quantity and the unit, such as
T cm Tcm just ‘cm’

17. Presentation of Data in graphs
It is expected that each axis will be labelled with the quantity (including unit) which is being plotted.
The quantity may be represented by a symbol or written in words. There must be some kind of distinguishing notation between the quantity and the unit.
Basically, just copy the column headings from your table directly on to your axis labels, including your units!