Chapter 1 Physical Quantities
a) Base and Derived quantities
b) Prefixes
c) Scalar & Vector
d) Estimation
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Physical Quantities
Any quantity that can be measured by an instrument or calculated
using a formula and has a unit
Time, t = 30.2 s
Physical
quantity
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symbol
SI unit
Magnitude
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1.1 Physical Quantities
Base Quantity
Derived Quantity
(Can be simplified in to base)
(Cannot be further be simplified)
•Work Done, J
•Charge, C
•Velocity, ms-1
•Pressure, Pa
•Temperature, K
•Power, W
•Resistance, Ω
•Current, A
•Force, N
•Volts, V
•Length, m
•Time, s
•Mass, kg
•Amount of substance, mol
•Etc
•Light intensity, candela
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1.2 Expressing derived units in terms of SI base units
e.g Newton, N
e.g Joules, J
Step 1: Select formula
Workdone = F x d
Step 2: put units until you get all
base quantities
= N x m
= kgms-2 x m
= kgm2s-2
F = ma
= kgms-2
or
Kinetic Energy =
1 m v2
2
=kg(ms-1)2
=kgm2s-2
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1.2 Expressing derived units in terms of SI base units
e.g Watts, W
Power =
e.g Pascal, Pa
Pressure =
Work done
Area
Time
=
=
J
=
kgm2s-2
=
kgm2s-3
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kgms-2
m2
s
=
N
m2
s
=
force
5
kgm-1s-2
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1.2 Expressing derived units in terms of SI base units
e.g Coulomb, C
e.g ohms, Ω
Resistance =
Charge = Current x
Potential difference
Time
Current
= As
=
V
A
e.g Volts, V
=
Potential difference = Work done
Charge
=
kgm2s-3A-1
A
kgm2s-2
=
As
kgm2s-3A-2
= kgm2s-3A-1
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1.2 Expressing derived units in terms of SI base units
Finding SI base units of unknown
e.g
F =
GMm
r2
Find SI base unit of G
Given that F = force
M and m = masses
r = distance
G = Fr2
Mm
= Nm2 = kgms-2m2 = kg-1m3s-2
kg2
kg2
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1.3 Homogeneity
For any equation in physics, they are
all homogenous which means SI base
units of each term should be same
s
u
a
t
=
=
=
=
s:
ut:
1 a t2:
2
s = ut + 1 a t2
2
Displacement
Velocity initial
acceleration
Time
SI base unit = m
SI base unit = ms-1xs
= m
SI base unit = ms-2xs2 = m
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1.4 Prefixes
Letters added before a unit to express large or small values
Prefixes
Symbol
Value
Tera
T
1012
Giga
G
109
Mega
M
106
kilo
k
103
Deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
µ
10-6
nano
n
10-9
pico
p
10-12
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Rules for prefixes
1. To remove a prefix multiply by its
value
2. To add a prefix divide by its value
3. For area and volume take square
and cube of prefix
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Examples on prefix
i) Convert 0.00983 Gm into m
iii) Convert 0.998 A into dA
= 0.00983 x 109
= 0.998
10-1
= 9.83 x 106 m
i) Convert 73000 µg into g
iv) Convert 12000 g into kg
= 73000 x 10-6
= 12000
= 12 kg
103
= 0.073 g
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= 9.98 dA
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1.1 Physical Quantities and measurement
Examples on prefix
vii) Convert 24 dm3 into cm3
v) Convert 12 cm into mm
= 12 x
= 24 x (10-1 )3
10-2
(10-2)3
10-3
= 120 mm
vi) Convert 1200 nm into µm
= 24000 cm3
viii) Convert 13000 mm2 into km2
= 13000 x( 10-3)2
= 1200 x 10-9
(103 )2
10-6
= 1.2 µm
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= 1.3 x 10
18
-8
km2
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1.3 Scalar and Vectors
Physical Quantities can be either scalar or vector
Scalars: such quantities only have magnitude and no direction
Distance,
Speed,
Time,
Temperature,
mass,
Energy
Representing scalar quantity:
Time, t = 30.2 s
Physical
quantity
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symbol
SI unit
Magnitude
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1.3 Scalar and Vectors
Vectors: Such quantities have magnitude and direction
e.g apply a force of 10 N
on following object
e.g apply a force of 10 N on
following object to right side
F = 10 N
F = 10 N
Force, F = 10 N to right side
If direction is not provided,
information will be
incomplete
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Physical
quantity
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SI Unit
Symbol
Magnitude
Direction
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1.3 Scalar and Vectors
6N
Common vector quantities
Displacement, Velocity,
30°
Force,
Acceleration, momentum
10°
9N
Representing a vector:
10 N
8N
6N
9N of force acting 10° to
west of North
8N of force acting to north
-6N
Length of arrow represents
magnitude
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6N of force acting 30°
to horizontal
- 8N
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8N of force acting to south
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1.2 Scalar and Vectors
Addition of vector quantities
to find a resultant force
2) Vectors in opposite direction
1) Vectors in same direction
12 N
6N
7N
10N
In opposite direction they are
subtracted
In same direction vectors are
always added
5 N
Resultant = 16N
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1.2 Scalar and Vectors
Addition of vector quantities
to find a resultant force
3) Vectors at an angle
E.g
600 N
800 N
+
30°
Maximum possible answer is 800 + 600 N = 1400 N
Minimum possible answer is 800 - 600 N = 200 N
For exact answer there are two methods: A) Head - to - tail rule
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B) Parallelogram rule
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1.2 Scalar and Vectors
A)Graphical method
Head-to-tail rule
Step1: Choose a scale
Step 4: measure the length of resultant
force
R = 13.53 cm
100 N : 1 cm
Step 2: Redraw the two vectors such
that head of one vector should touch
the tail of the vector
Step 5: convert cm into Newtons
6 cm
R = 1353 N
30°
8 cm
Step 6: Measure angle of resultant
with a horizontal
Step 3: Draw resultant from tail to
head to complete the triangle
Resultant is 1350 N acting
13° to horizontal
6 cm
13°
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30°
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1.2 Scalar and Vectors
E.g
Scale:
40 N
10 N : 1 cm
4 cm
39°
3 cm
+
5 cm
30 N
Resultant 50 N acting 39° to horizontal
(Maximum = 70 N,
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Note:
for right angle triangle vectors you
may use Pythagorus theorem
Minimum = 10 N)
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h2 = p2 + b2
h2 = 302 + 402
h2 = 2500
h = Yousuf
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1.2 Scalar and Vectors
A)Graphical method
Parallelogram rule
30 N
40 N
+
60°
Maximum possible answer is 30 + 40 N = 70 N
Minimum possible answer is 40 - 30 N = 10 N
For exact answer few steps have to be followed in parallelogram rule
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1.2 Scalar and Vectors
6 cm
A) Graphical method
( parallelogram rule)
Step1: Choose a scale
8 cm
5 N : 1 cm
74°
Step 2: Redraw the two vectors such
that the two tails are touched
8 cm
60°
6 cm
Step 4: Draw resultant from two tails
to the two heads
Step 5: Measure length of resultant
and convert cm in N R = 7.21 cm
5 N : 1 cm
R = 36.0 N
R : 7.21 cm
8 cm
60°
6 cm
Step 6: Measure angle of resultant
with a horizontal
Step 3: Draw parallel vectors to
complete a parallelogram
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Resultant is 36.0 N acting
74° to horizontal
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1.2 Scalar and Vectors
600 N
30°
B) Geometrical method
Head to tail rule
800 N
Step2: Apply cos rule to find R:
When two sides and including angle is
given opposite side can be calculated
800 N
+
a
600 N
b2 = a2 +c2 - 2ac CosB
B
c
30°
R
150°
Step1:
Redraw the two vectors using head to
tail rule ( without any use of scale)
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b
600 N
30°
800 N
R2 = 8002 +6002 - 2x800x600 Cos150
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R = 1353 N
= 1350 N
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Sin
600
Step3:
Apply sin rule to find angle of R
= Sin 150
1353
=
a
12.8
b
C
B
A
c
Final answer:
Sin A = Sin B = Sin C
a
b
c
R = 1353
150°
1350 N acting 12.8°
600 N
30°
800 N
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𝜽
𝜽𝜽
1.2 Scalar and Vectors
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1.2 Scalar and Vectors
Resolution of vectors into two
perpendicular components
R = 450N
50°
R = 450N
Rx
Sin 50 =
50°
Step 1: Draw two vectors
perpendicular to one another
using head to tail so that
resultant shown can be drawn
out of it
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Ry
Ry
Cos 50
450
Ry = 450Sin50
= 344.7 N
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= Rx
450
Rx = 450cos50
= 289.3 N
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1.2 Scalar and Vectors
R = 800N
Further examples on
resolution
R = 450N
Ry
15°
Ry
85°
Rx
Sin 15 =
Ry
Rx
Cos 15
450
Ry
= 450Sin15
= 116.4 N
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Sin 85 =
= Rx
Cos 85 = Rx
800
450
Rx
Ry
Ry
= 450cos15
= 800Sin85
= 797 N
= 434.7 N
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800
Rx
= 800cos85
= 69.7 N
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1.2 Scalar and Vectors
70 N
40 N
Ry
= 40 N
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Rx
Ry
=0 N
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=0
Rx
= 70 N
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1.2 Scalar and Vectors
Rx
Note: for a right angle triangle
Perpendicular is always the side
that is opposite to angle under
consideration
Ry 35°
R = 450N
Base is the side that is adjacent
to angle under consideration
Sin 35 =
Rx
Cos 35 =
450
Rx
= 450Sin35
= 258.1
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Ry
450
Ry
= 450Cos35
= 368.6
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1.2 Scalar and Vectors
Shortcut to find component
The axis with which angle is given is
always the cos component and the
other axis becomes the sin component
Ry
35°
R = 450N
Ry
Rx
50°
Ry = 450 cos35
Rx = 450 sin35
Rx
Rx = 450 cos50
R
=
450
sin50
y
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= 289.3
= 344.7
R = 450N
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= 368.6 N
= 258.1 N
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1.2 Scalar and Vectors
Step 2:
Add horizontal components
Rx = 800 + 519
A = 800 N
= 1319 N
Step 3:
+
Add vertical components
B = 600 N
Ry = 0 + 300
= 300 N
Step 4: Find resultant using pythogrous
theorem
30°
R2 = 13192 + 3002 = 1352 N
Steps 1: resolve every vector in
to perpendicular components
Ax =
Ay =
800 N
0
𝜽
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𝜽
𝜽
C) Addition of vectors using
perpendicular components
Bx =
By =
Step 5: find
R = 1352
300
600cos30 = 519
600sin30 = 300
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1319
Tan
= 300
1319
= 12.8°
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1.3 Estimation
Foot ball = 10.0 cm
A) Masses
Earth = 6400 km
hydrogen atom= 10-27 kg
rain drop = 0.03 g
C) Density
coin = 2 g
Water= 1gcm-3 or 1000 kgm-3
Meter rule / apple = 150g
Steel = 8 gcm-3 or 8000 kgm-3
adult person = 70 kg
family car = 1500 kg
D) Speed
lorry = 4000 kg
Sound in air = 330 ms-1
Light in vacuum = 3 x 108 ms-1
B) Radius
Olympic runner = 10 ms-1
Atom = 10-10 m
Golf ball= 2.3 cm
Tennis ball = 3.5 cm
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1.3 Estimation
E) Wavelength
E) Time taken
D) Frequencies/Hz
Gamma-rays
X-rays
Ultraviolet
Visible
Infrared
Microwaves
Radio waves
Gamma-rays
X-rays
Ultraviolet
Visible
Infrared
Microwaves
Radio waves
Violet:
Blue:
Green:
Yellow:
Orange:
Red:
Average life span of a person: 70 years
Light to reach sun to earth: 8 minutes
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1020 – 1024
1017 – 1020
1015 – 1017
4 x 1014 – 7.5 x 1014
1013 – 1014
3 x 1011 – 1013
<3 x 1011
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< 10-12 m
1 nm – 1 pm
400 nm – 1 nm
750 nm – 400 nm
25 μm – 2.5 μm
1 mm – 25 μm
> 1 mm
380–450 nm
450–495 nm
495–570 nm
570–590 nm
590–620 nm
620–750 nm
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1.3 Estimation
I) Atmospheric Pressure
F) Resistivity,
1.01 x 105 Pa
Copper: 1.77 × 10-8 ohm-metre
G) number density, n
Copper: 8.5 × 1028 m-3
H) Young Modulus, E
Steel: 1.90 x 1011 Pa
Copper: 1.10 x 1011 Pa
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𝝆
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