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Introduction to Physics I
Understanding Base and Derived Quantities
Physical Quantity
1. A physical quantity is a quantity that can
be measured.
2. Physical quantities are usually expressed
as the product of a numerical value and a
physical unit
Example
2
2.34 10
E kJ
= ×
where
• E represents the physical quantity of
energy
•
2
2.34 10
× is the numerical value
• k is the SI prefix kilo representing 103
• J is the symbol for the unit of energy,
the joule
3. A physical quantity can be divided into
base quantity and derived quantity.
Base quantity
1. Base quantities are the quantities that are
conventionally accepted as functionally
independent of one another.
2. It is a quantity that cannot be defined in
term of other physical quantity.
3. The base Quantities and its units are as
below:
Quantity Name of
unit
Unit
symbol
Length metre m
Mass kilogram kg
Time second s
Electric current ampere A
Thermodynamic
temperature
Kelvin K
Amount of
substance
mole mol
Luminous
intensity
candela cd
[Notes: Amount of substance and Luminous
intensity are not discussed in SPM physics
syllabus.]
The SI base units are defined as follows:
Unit Definition
metre The metre is the length of the
path travelled by light in vacuum
during a time interval of 1/299
792 458 of a second.
kilogram The kilogram is the unit of mass;
it is equal to the mass of the
international prototype of the
kilogram.
second The second is 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 The ampere is that constant
current which, if maintained in
two straight parallel conductors
of infinite length, of negligible
circular cross-section, and placed
1 metre apart in vacuum, would
produce between these
conductors a force equal to 2 ×
10−7 newton per metre of length.
kelvin The Kelvin, unit of
thermodynamic temperature, is
the fraction 1/273.16 of the
thermodynamic temperature of
the triple point of water.
mole The mole is the amount of
substance of a system which
contains as many elementary
entities as there are atoms in
0.012 kilogram 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.
[Notes: The definitions of the units are only
served as an additional note, it is not
discussed in the SPM syllabus.]

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Exercise 1
1. Which of the following quantity is not a
base quantity?
A Length
B Mass
C Current
D Force
2. Which of the following quantity is base
quantity?
A Temperature
B Force
C Volume
D Charge
3. Which of the following units is not a SI
base unit?
A Kelvin
B Newton
C Kilogram
D Ampere
4. The unit of mass which defined in SI
system is
A Gram
B Kilogram
C Pound
D Kilopound
5. Which of the following is true?
kilogram gram
A Multiple of base
unit
Multiple of base
unit
B Base unit Base unit
C Multiple of base
unit
Base unit
D Base unit Multiple of base
unit
Answer
Scientific notation (Standard form)
1. Scientific notation (also known as Standard index notation) is a convenient way to write very
small or large numbers.
2. In this notation, numbers are separated into two parts, a real number with an absolute value
between 1 and 10 and an order of magnitude value written as a power of 10.
3. Physical quantities that are very big or very small need to be written in the standard form so that
it is neat, simple and easy to read.
Example:
Numerical value Standard form
6 020 000 000 000 000 kg
0.000 000 000 074 m
Significant Figure
1. In measurement, significant figures relate the certainty of the measurement.
2. As the number of significant figures increases, the certainty of the measurement increase, which
means we are more certain about what we have measured.

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3. In the SPM syllabus, the magnitude of a physical quantity is usually rounded up to 3 or 4
significant figures.
Example:
speed of light in a vacuum = 299 792 458 ms-1
= 3.00 × 108
ms-1
(to 3 significant figures)
Exercise 2
1. Write down the significance figure (s.f.) of the following value:
a. 135 m, (____s.f.)
b. 0.013s (____s.f.)
c. 0.2000A (____s.f.)
d. 25.10 g (____s.f.)
e. 3700km (____s.f.)
f. 0.003kg (____s.f.)
g. 1.54 × 10-3
(____s.f.)
i. 0.001200 (____s.f.)
2. Round up the following number to the number of significance figure (s.f.) that given in the
bracket.
a. 235478 [3s.f.]
b. 230008 [3s.f.]
c. 12.4369 [4s.f.]
d. 0.00216 [1s.f.]
e. 134.016 [2s.f.]
Prefixes
Prefixes are the preceding factor used to represent very small and very large physical quantities in
SI units.
Prefixes Value Standard form Symbol
Tera 1 000 000 000 000 1012
T
Giga 1 000 000 000 109
G
Mega 1 000 000 106
M
Kilo 1 000 103
k
deci 0.1 10-1
d
centi 0.01 10-2
c
milli 0.001 10-3
m
micro 0.000 001 10-6
μ
nano 0.000 000 001 10-9
n
pico 0.000 000 000 001 10-12
p
Conversion of prefixes
Prefixes to Numerical Value
Example 1
The frequency of the radio wave is 210M Hz.
What is the frequency of the radio wave in Hz?
Example 2
The thickness of a film is 245nm. What is the
thickness in unit meter?
Numerical Value to Prefixes
Example 3
0.306 s is equal to how many ms.
Example 4
Convert 0.00034W into µW.

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Prefixes to Prefixes
Example 5
Convert 0.000012 km into cm.
Example 6
Convert 630,000,000 J into kJ.
Example 7
Arrange the following values in ascending
order.
3
2.32 10 Mm
−
× 4
2.32 10 cm
×
7
2.32 10 m
μ
× 4
2.32 10 km
−
×
Answer
3
2.32 10 Mm
−
× =
7
2.32 10 m
μ
× =
4
2.32 10 cm
× =
4
2.32 10 km
−
× =
Units for Area and Volume
Example 8
a) 7.2 m = ____________cm
b) 0.32 m2
= ____________cm2
c) 0.0012 m3
= ____________cm3
d) 5.6 cm = ____________m
e) 350 cm2
= ____________m2
f) 45000 cm3
= ____________m3
Exercise 3
1. Convert each of the following measurements into metre ( m ).
a) 12000 μm
b) 230 mm
c) 0.34 km
d) 0.012 Mm
2. Complete the following unit convertion
a) 12.34 kHz = ___________ Hz
b) 120 Mm = ___________m
c) 0.12 μg = ___________g
d) 7.1×103
mJ = ___________J
e) 8.34×10-1
cA = ___________A
f) 5.1×102 dW = ___________W
g) 1.11×10-3
nm = ___________m
h) 7.134 ×104
pm= ___________m
i) 14500 g = ___________kg
j) 12.34 N = ___________MN
k) 0.134 s = ___________ ms
l) 756.6 Hz = ___________ kHz
m) 0.00034 J = ___________ μJ
n) 3.12 A = ___________d A
o) 134 kg = ___________mg
p) 1117 nHz = ___________μHz
q) 0.230 km = ___________μm
r) 0.012 MJ = ___________kJ
1 m = ______ cm
1 m2
= ______ cm2
1 m3
= ______ cm3
1 cm = ______ m
1 cm2
= ______ m2
1 cm3
= ______ m3
1 m = 100cm
1 m2
= 1m × 1m
= 100cm × 100cm
= 10 000 cm2
= 1 × 104
cm2
1 m3
= 1m × 1m × 1m
= 100cm × 100cm × 100cm
= 1 000 000 cm3
= 1 × 106
cm3

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3. Complete the following unit conversion
a) 13 m = ____________cm
b) 12.1 m2
= ____________cm2
c) 0.1 m3
= ____________cm3
d) 12.1 cm = ____________m
e) 1200 cm2
= ____________m2
f) 130 cm3
= ____________m3
g) 3.55 m2
= ____________cm2
h) 1200 m2
= ____________cm2
i) 1000 m3
= ____________cm3
j) 1.2×102m3
= ____________cm3
k) 5.34×105cm2
= ____________m2
l) 7230 cm2
= ____________m2
m) 9.8×10-1cm3
= ____________m3
n) 800 cm3
= ____________m3
o) 7×10-3
cm = ____________m
4. Which of the following sets of prefixes
are arranged in descending order?
A mili, centi, micro
B mega, micro, gega
C kilo, mili, centi
D kilo, mili, nano
5. Which of the following length is the
longest?
A 7.1×103
cm
B 6.4×105
μm
C 4.2×10-3
km
D 9.8×10-7
Mm
6. Which of the following unit conversions
is not correct?
A 230 Ms = 2.3 × 108
s
B 360 μs = 3.6 × 10-4
s
C 0.0013s = 1.3 ms
D 2.34 × 105
s = 23.4 ks
7. Among the quantity below, which one is
equivalent to 0.000360 m?
A 360 km
B 360 cm
C 360 mm
D 360 µm
8. 0.34km is equivalent to
A 3.4 × 104
cm
B 3.4 × 10-3
Mm
C 3.4 × 106
mm
D 3.4 × 103
m
9. The standard form of 540μK is
A 5.40 × 102
K
B 5.40 × 10 K
C 5.40 × 10-6
K
D 5.40 × 10-3
K
E 5.40 × 10-4
K
10. Which of the following unit conversions
is correct?
A 2.5 m2
= 250 cm2
B 5.6 m3
= 560 cm2
C 4500 cm2
= 45 m2
D 2.5 × 107
cm3
= 25 m3
11. The dimension of cuboids is 20cm, 25cm
and 30cm. The volume of the cuboids is.
A 1.5 × 10-2
m3
B 1.5 m3
C 1.5 × 102
m3
D 1.5 × 104
m3
12. The dimension of cuboids is 10cm, 20cm
and 20cm. The total surface area of the
cuboids is.
A 1600 m2
B 16 m2
C 1.6 m2
D 0.16 m2
Answer
1. 4. 7. 10.
2. 5. 8. 11.
3. 6. 9. 12.
Derived Quantity
1. A derived quantity is a Physics quantity that is not a base quantity. It is the quantities which
derived from the base quantities through multiplying and/or dividing them.
Example
Area of a rectangle = length of the rectangle × width of the rectangle
2. The length and width of the rectangle are base quantity whereas the area of the rectangle is a
derived quantity. It is derived from the product of two base quantities.

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Example
State whether the following quantities in the equation are base or derived quantity.
Equation Quantity
Distance = ___________ quantity
Time = ___________ quantity
Time
Distance
Speed =
Speed = ____________ quantity
Example of derived quantities
Quantity Equation Unit Unit symbol
Area Area = length × width square metre m2
Volume Volume = length × width × height cubic metre m3
Frequency 1
frequency
period
=
hertz Hz s−1
Density mass
density
volume
=
kilogram per
cubic metre
kg m−3
Velocity/speed displacement
velocity
time
=
metre per
second
m s−1
Acceleration velocity change
acceleration
time
=
meters per
second squared
m s−2
Force Force = mass × acceleration Newton N m kg
s−2
Pressure, stress force
pressure
area
=
Pascal Pa N m−2
Energy, work Work = force × displacement Joule J N m
Power work
power
time
=
Watt W J s−1
Quantity of
electricity
Quantity of charge = current × time Coulomb C A s
Potential
difference,
electromotive
force
arg
energy
potential difference
ch e
=
Volt V WA−1
Electric
resistance
potential difference
resistance=
current
Ohm Ω VA−1
Unit
A unit is a particular physical quantity,
defined and adopted by convention, with
which other particular quantities of the same
kind are compared to express their value.
SI unit
The International System of Units
(abbreviated SI from the French language
name Système International d'Unités) is the
modern form of the metric system.
It is the world's most widely used system of
units, both in everyday commerce and in
science.

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Example 6
Which of the physical quantity below has
correct S.I. unit?
Physical
Quantity
S.I. unit
A Length Centimeter
B Mass Gram
C Time Minute
D Current Ampere
Derived Unit
1. The derived unit is a combination of base
units through multiplying and/or dividing
them.
For instance,
Speed is defined as the rate of distance
change, and can be written in the
mathematic form
Time
Distance
Speed =
The base unit for distance (length) is
metre (m) and
The base unit for time is second (s).
Therefore,
The unit of speed
1
( )
( )
m
ms
s
−
= =
2. Sometime, the units are named after great
physicist to honour their significant
contributions to the field of physics.
3. For example Newton, N, which is the unit
of force, is named after Sir Isaac Newton,
who contributed a lot to the classical
mechanic.
Find the derived unit
Example 7
Derive the units for the following quantities
a) Acceleration
b) Density
c) Work
d) Charge
e) Potential difference
Hint
velocity change
acceleration
time
=
mass
density
volume
=
Work = force × displacement
Quantity of charge = current × time
arg
energy
potential difference
ch e
=
Example 8
The moment inertia of a disc is given by
equation
2
2
1
mr
I =
m = mass of the disc and r = its radius.
Find the unit of moment inertia, I.
Find the unit of a constant in an equation
Example 9
The relationship of the mass of a metal plat
with its area is given by the equation
mass = k × area
What is the unit of k?

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Unit conversion
Example 9
A car is moving with speed 2km minute-1
,
what is the speed in m s-1
?
Example 10
Complete the following unit conversion
a) 12 kmh-1
= __________ ms-1
b) 12 ms-1
= __________ kmh-1
c) 12 kgm-3
= __________ gcm-3
d) 0.2 gcm-3
= __________ kgm-3
e) 0.000012 kg m s-2
= _________g cm s-2
Convert the SI unit to its base unit
Write the following unit in an appropriate
base unit:
a) 3 J =
b) 2 N=
Summary
Physical quantities A physical quantity is a quantity that can be measured.
Base quantity Base quantities are the quantities that are conventionally accepted as
functionally independent of one another.
Derive Quantity A derived quantity is a Physics quantity that is not a base quantity. It is the
quantities which derived from the base quantities.
Unit A unit is a particular physical quantity, defined and adopted by convention,
with which other particular quantities of the same kind are compared to
express their value.
Exercise 4
1. Which of the followings is a derived
quantity?
A Charge
B Current
C Temperature
D Length
2. Which of the following quantities is not
derived from the base quantity of time?
A Force
B Density
C Pressure
D Speed
3. Which of the followings is a derived unit?
A metre2
B Kelvin
C gram
D second
4. Which of the following is not a derive
unit?
A Newton
B Kelvin
C Watt
D Joule

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5. Which of the derived units below is
correct for the given quantities?
displacement velocity acceleration
A ms-2
m ms-1
B m ms ms-2
C m ms-2
ms-1
D m ms-1
ms-2
6. The unit of force, Newton (N) is
equivalent to
A kg ms-1
B kg m2
s-2
C kg ms-2
D kg2
ms-2
7. The derived unit kg s-2
is equivalent to
A N m-1
B g s-1
C kg s-1
D N cm-2
8. Which of the following is the unit of
density?
[Hint:
mass
density
volume
= ]
A kg m3
B kg m2
C kg m-3
D kg m-2
9. Which of the following derived units is
wrong?
Derived Quantity S.I. unit
A Acceleration ms-2
B Density kg m-3
C Pressure kg m-2
D Work kg m2
s-2
10. Given that the mass and the volume of an
ice cube is as below
Mass = 0.45kg
Volume = 500 cm3
Find the density of the ice in kg m-3
.
[Notes:
mass
density
volume
= ]
11. The relationship of pressure (P), force (F)
and area (A) is given by the
equation
F
P
A
= . Find the value of
pressure when the force = 500N and the
area = 10000 cm2
.
12. The elastic potential energy (US) that
store in a spring is given by the formula
2
1
2
s
U kx
= , where k is the coefficient of
the spring and x is the extension of the
spring. The unit of k is
A J m-1
B kg s-2
C J m2
D kg m2
s-2
13. The specific heat capacity of a substance
(c) if given by the equation
E
c
mθ
=
Where E = heat change (Energy)
m = mass of substance
θ = temperature change
Find the unit of specific heat capacity, c
A J kg K-1
B J kg-1
K
C J kg K-2
D J kg-1
K-1

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14. Find the unit of following Derive quantity.
a) Acceleration
(
velocity change
time taken
acceleration = )
b) Momentum (momentum = mass ×
velocity)
c) Impulse (impulse = change of momentum)
d) Density (
mass
density
volume
= )
e) Force (Force = mass × acceleration)
f) Pressure (
force
pressure
area
= )
g) Electric Charge (electric charge = current
× time)
15. Complete the following unit conversion
of speed.
a) 90 kmh-1
= __________ ms-1
b) 110 kmh-1
= __________ ms-1
c) 1.3 ms-1
= __________ kmh-1
d) 8.12 ms-1
= __________ kmh-1
16. Complete the following unit conversion
of density.
a) 760 kgm-3
= __________ gcm-3
b) 12000 kgm-3
= __________ gcm-3
c) 5.1 gcm-3
= __________ kgm-3
d) 3600 Nm-2
= __________ Ncm-2
e) 12×106
Nm-2
= __________ Ncm-2
f) 1.5×10+ Nm-2
= __________ Ncm-2
g) 3.16×10-5
Ncm-2
= __________ Nm-2
h) 7.1×10-3
Ncm-2
= __________ Nm-2
17. Convert 4500kJ/hour to Watt (J/s).
A 1250 W
B 1.25W
C 75W
D 75 000W