Tutorial 1

Using Symbols

An equation is a mathematical model that sums up how a system behaves.  For example, we know that, if we have a current flowing through a wire and double the voltage, the current will double as well.  We know that the quantities of current and voltage are related by the simple rule:

V = IR

In physics problems we are given certain quantities and we have to use them to find an unknown quantity with an equation.  In all problems in AS level, you will only ever have ONE unknown.  You will never be expected to tackle a problem with two or more unknowns.  That said, you may need to look up some quantities from the data sheet.

 

In GCSE you were often given equations in words:

Distance (m) = speed (m/s) × time (s)

You will notice from the data sheet at the end of these notes that the equations are given in symbols, which in my notes I refer to as Physics Code.  The symbols all mean something; they are abbreviations.  The symbols used in exams and most textbooks are those agreed by the Association of Science Education.

Some symbols are easy; V stands for voltage.  Some are not so easy.  I for current comes from the French intensité du courant, since it was a French physicist who first worked on it.  In print you will always find the codes written in italics.  In my notes, I do try to, but sometimes I miss it.  As you can’t do italics in normal handwriting, then don’t worry.  Here are some examples:

 a

Acceleration

 A

Area

 F

Force

 m

Mass

 I

Current

 p

Pressure

 Q

Charge

 

1. This question is about Physics codes.  What do they refer to?
  1. F = ma
  2. E = 1/2 mv2
  3. c = f.

Answer

 

You will come across codes written in Greek letters.  The normal (Latin) alphabet has 26 characters.  No codes are used which are like ä (a – umlaut) or ê (e – circumflex). The Greek alphabet adds another 24.  The Greek Alphabet is this:

Greek

Name

Letter

Greek

Name

Letter

a

alpha

a

n

nu

n

b

beta

b

x

xi

x

g

gamma

g

o

omicron

Short o (ŏ)

d (D)

delta

d (D)

p

pi

p

e

epsilon

Short e (ĕ)

r

rho

r

z

zeta

z

s (S)

sigma

s (S)

h

eta

Long e (ē)

t

tau

t

q

theta

th

u

upsilon

u

i

iota

i

f (F)

phi

ph [or f (F)]

k

kappa

k

c

chi

ch

l (L)

lambda

l (L)

y (Y)

psi

ps

m

mu

m

w (W)

omega

Long o [ō (Ō)]

 

Some quantities share the same physics codes, e.g. Q for charge, and Q for energy.  You will need to be aware of this when you do the exam, and knowing what each code stands for is part of your examination preparation.

 

Units

Physics formulae use SI (Système International) units based on seven base units:

Many physics formulae will give you the right answer ONLY if you put the quantities in SI units.  This means that you have to convert.  You will often find units that are prefixed, for example kilometre.  The table below shows you the commonest prefixes and what they mean:

Prefix

Symbol

Meaning

Example

pico

p

´ 10-12

1 pF

nano

n

´ 10-9

1 nF

micro

m

´ 10-6

1 mg

milli

m

´ 10-3

1 mm

centi

c

´ 10-2

1 cm

kilo

k

´ 103

1 km

Mega

M

´ 106

1 MW

Giga

G

´ 109

1 GWh

 

This little character is about to walk into a bear trap.  In the notes you will see him where there are common bear traps such as failing to convert into SI units.

When you write out your answer, you must always put the correct unit at the end.  The number 2500 on its own is meaningless; 2500 J gives it a meaning.

2. Convert the following quantities to SI units:
  • 15 cm
  • 500 g

  • 3 km

  • 35 mV

  • 220 nF

Answer

 

Many units are made up from base units.  They are sometimes called derived units.  We all know that force is measured in Newtons.  We also know the familiar equation for force:

Force (N) = mass (kg) × acceleration (m s-2)

We multiply the units for mass (kg) and acceleration to give kg m s-2.  Therefore 1 N = 1 kg m s-2.

Note:

While it is perfectly OK to write the units for speed as m/s (metres per second), we should get into the habit of writing m s-1.  Note also the need for a space between the 'm' and the 's'.  If we write ms-1 it actually means "milliseconds to the minus one".

 

Unit analysis is not part of the syllabus, but it is a useful technique for understanding the relationship between units.

 

3. Convert the following quantities to SI units or non-SI units as appropriate:

     1 m2                                                                                 

     

     to mm2

     0.45 mm2                                                                            

     

     to m2

     1 cm3                                                                           

     

    to m3

     22.4 dm3                                                             

     

    to m3

Answer