OBJECTIVES
1. Ability to define and understand base and
derived quantities, distinguish standard
units and system of unit, and fundamental
quantities.
2. Ability to understand and apply converting
units within a system or from one system
of unit to another
3. Ability to understand and apply
Dimensional Analysis.
DEFINITION
a physical quantity that can be
counted or measured using
standard size defined by custom
or law.
Every measurement or quantitative statement
requires a unit.
Example:
If you say you’re driving a car 30 that doesn't mean
anything. Are you driving it 30 miles/hour, 30 km/hour,
or 30 ft/sec? 30 only means something when unit is
attached to it.
STANDARD UNITS
• If a unit becomes officially accepted, it’s
called Standard Unit.
• Group of Unit and Combination is called
SYSTEM OF UNITS.
Example: SI Units, British Units
SI = International Systems of Units
• SI (Système International) Units also
called Metric System
MKS system
CGS System
L = meters (m)
centimeter (cm)
M = kilograms (kg)
gram (g)
T = seconds (s)
seconds (s)
• All things in classical mechanics can be
expressed in terms of base quantities:
– Length (L) , MASS (M), TIME (T)
 British Units:
L = inches, feet,
miles,
M = slugs (pounds),
T = seconds
PHYSICAL QUANTITIES
- Physics is based on physical quantities. Eg: length,
mass, time, force and pressure.
- Generally, physical quantity is a quantity that can be
measured.
Physical quantities
Definition
Base quantities
Fundamental quantities having their
own dimensions. Eg: length, mass,
time, electrical current, etc.
Derived quantities
The quantity which derived from base
quantity. Eg: force, energy, pressure,
etc
BASE QUANTITIES IN SI
SYSTEM
Name
Symbol of
quantity
Symbol of
dimension
SI base unit
Length
l
L
meter (m)
Time
t
T
second (s)
Mass
m
M
kilogram (kg)
Electrical
current
I
I
Ampere (A)
Thermodynami
c temperature
T

Kelvin (K)
Amount of
substance
n
N
mole
Luminous
intensity
Iv
J
Candela (c)
DERIVED QUANTITIES
FROM BASE QUANTITIES
Quantity
Name
Symbol
of
quantity
SI unit
Symbol of
dimension
Force, Weight
Newton
N
mkg/s2
LMT-2
Energy, Work,
Heat
Joule
J
m2kg/s2
L2MT-2
Power, radian flux
Watt
W
m2kg/s3
L2MT-3
Frequency
Hertz
Hz
s-1
T-1
Pressure, Stress
Pascal
Pa
m-1kg/s2
L-1MT-2
Electric charge or
flux
Coulomb
C
As
AT
Electrical potential
difference
Volt
V
m2∙kg∙s−3∙A−1
L2MT-3A-1
Quantity
Name
Symbol of
quantity
SI unit
Symbol of
dimension
Electric
resistance,
Impedance,
Reactance
Ohm
Ω
m2kgs−3A−2
L2MT-3A-2
Electric
capacitance
Farad
F
m−2kg−1s4A2
L-2M-1T4A2
Magnetic flux
density,
magnetic
induction
Tesla
T
kgs−2A−1
MT-2A-1
Magnetic flux
Weber
W
m2kgs−2A−1
L2MT-2A-1
Inductance
Henry
H
m2kgs−2A−2
L2MT-2A-2
DIMENSION
• From Latin word = "measured out"
a parameter or measurement required to
define the characteristics of an object - i.e.
length, width, and height or size and shape.
What are their units, dimensions and values?
- 110 mg of sodium
- 24 hands high
- 5 gal of gasoline
DIMENSIONAL ANALYSIS
• PURPOSES:
1) TO CHECK THE EQUATION
2) ANALYSIS DIMENSION TO BUILD FORMULA
• Example (to check equation):
Distance, d=vt2 ( velocity x time2 )
– Dimension on left side [d] = L
– Dimension on right side [vt2] = L / T x T2 = L x T
– L=LT? Left units and right units don’t match, the
equation must be wrong !!
Example 1
The force (F) to keep an object moving in a circle can be
described in terms of the velocity, v, (dimension L/T) of the
object, its mass, m, (dimension M), and the radius of the
circle, R, (dimension L).
– Which of the following formulas for F could be correct ?
(a)
F = mvR
(b) F  m v 
 
R
Remember: Force has dimensions of ML/T2
2
(c)
mv 2
F
R
Solution
(a)
F = mvR
(b)
v
F  m 
R
Consider for RHS, since [F] = MLT-2
For (a);
[mvR] = MLT-1L=ML2T-1 (incorrect)
For (b);
[mv2R-2] = ML2T-2L-2 = MT-2 (incorrect)
For (c);
[mv2R-1] = ML2T-2L-1 = MLT-2 (correct)
Answer is (c)
2
(c)
mv2
F
R
UNIT CONVERSIONS
• To change units in different systems, or different units
in the same system.
• Example:
Units in Different System
Units in the Same System
1 inch = 2.54 cm
(British  SI)
1 mile = 1.61 km
(British  SI)
1 yard = 1ft (British)
1kg= 1000g
(M.K.S to C.G.S in SI)
Example 2
• A hall bulletin board has an area of 2.5 m2. What is area in
cm2?
Solution:
conversion of area units (in the same SI unit: mks  cgs).
1m = 100cm.So,
2
 10 cm  10 4 cm 2

 
2
1
m
1
m


2
4
2
10
cm
4
2
2.5m 2 

2
.
5

10
cm
1m 2
Example 3
Convert miles per hour to meters per second.
Given:
– 1 inch
– 1m
– 1 mile
– 1 mile =
= 2.54 cm
= 3.28 ft
= 5280 ft
1.61 km
Solution:
mi 1mi 5280 ft
1m
1hr
m 1m
1 



 0.447 
hr hr
mi
3.28 ft 3600 s
s 2s
QUIZ 1
When on travel in Kedah you rent a small car
which consumes 6 liters of gasoline per 100
km. What is the MPG (mile per gallons) of
the car ?
1L=1000cm3=0.3531ft3,
1ft3=0.02832m3=7.481 gal
SIGNIFICANT FIGURES
• The number of digits that matter in a measurement or calculation.
1. all non-zero digits are significant.
2. in scientific notation all digits are significant
3. Zeros may or may not be significant.
• those used to position the decimal point are not significant.
• those used to position powers of ten ordinals may or may not
be significant.
• Examples:
– 2
– 40
– 4.0 x 101
– 0.0031
– 3.03
1 sig fig
ambiguous, could be 1 or 2 sig figs
2 sig figs (scientific notation)
2 sig figs
3 sig figs
• When multiplying or dividing, the answer should have the
same number of significant figures as the least accurate of the
quantities in the calculation.
• When adding or subtracting, the number of digits to the right
of the decimal point should equal that of the term in the sum
or difference that has the smallest number of digits to the
right of the decimal point.
• Examples:
– 2 x 3.1 = 6
– 3.1 + 0.004 = 3.1
– 4.0 x 101  2.04 x 102 = 1.6 X 10-1