Week - 1 - Consistency of Units
System of units-
Units are the standard for taking measurements of a quantity which is accepted by people all over the world such as foot, pound, centi-meter, gram, second, etc.
Basically, there are two types of system of units classified;
Fundamental Units:
These are the units of basic quantities that means units of length, mass and time.
There are following type of Fundamental Units are used in the measurement;
- SI System of Units (Standard International System)
This system has six basic units, two supplementary units and twenty-seven derived units. The basic units are as follows;
- FPS System of Units (Foot, Pound, Second)
- CGS System of Units (Centi-meter, Gram, Second)
- MKS System of Units (Mater, Kilogram, Second)
Derived Units:
These type of system of units are used to express quantity by combining two or more basic Fundamental Units Such as area, volume, capacity.
Conversion of S.I Unit to gm, mm, ms:
MASS 1 kg 1000 g conversion factor 103
LENGTH 1 m 1000 mm conversion factor 103
SEC 1 sec 1000 ms conversion factor 103
FORCE 1N Force = Mass X Acceleration
= 1 kg .m/s2 = (1000 g X 1000 mm)/ 1000 ms2 = 1 g.mm/ms2
Conversion factor 1
STRESS 1 Pa 1 Pa = 1 N/m2
= 1 (kg .m/s2)/ m2= {(1000 g X 1000 mm) / 1000 ms2}/ (1000 mm2)
= 10-6 g / mm.ms2
Conversion factor 10-6
ENERGY 1 N.m 1 N.m = 1 (kg .m/s2). m
= {(1000 g X 1000 mm) / 1000 ms2}/ (1000 mm)
= 103 g mm2/ms2
Conversion factor 103
DENSITY 1 kg/m3 1 kg/m3 = 1000 g / 1000 mm3
= 10-6 g/mm3
Conversion factor 10-6
YOUNG MODULUS 210GPA 1 Pa = 1 N/m2
= 1 (kg .m/s2)/ m2= {(1000 g X 1000 mm) / 1000 ms2}/ (1000 mm2)
= 10-6 g / mm.ms2
Conversion factor 10-6
So, 210 GPA = 210 X 109 PA = 210 X 109 X 10-6 = 210 X 103 g/mm.ms2
VELOCITY 56.33 KMPH 1Km = 106 mm 1 Hrs = 60 min = 3600 sec =36 X 105 ms
Km / Hr = 106 mm / 36 X 105 ms = 0.277 mm/ms
Conversion Factor 1
So, 56.33 KMPH = 56.33 X 0.277 = 15.60 mm/ms
GRAVITY 9.8 m/s2 1 m/s2 = 1000 mm/ 1000 ms2
= 10-3 mm/ms2
Conversion factor 10-3
So, 9.81 m/s2 = 9.81 X 10-3 mm/ms2
Conversion of S.I Unit to other units system (Note: Table based on conversion factor):
|
SI Units |
Mass (1kg) |
Length (1m) |
Time (1sec) |
Force (1N) |
Stress (1 Pa) |
Energy (1N.m) |
Density (1 kg/m3) |
Young Modulus (210 GPA) |
Velocity 56.33kmph (15.67m/s) |
Gravity 9.81 m/s2 |
|
g,mm,ms |
103 |
103 |
103 |
1 |
10-6 |
103 |
10-6 |
10-6 |
1 |
10-3 |
|
Kg,cm,ms |
1 |
102 |
103 |
10-4 |
10-8 |
10-2 |
10-6 |
10-8 |
10-1 |
10-4 |
|
Kg,cm,s |
1 |
102 |
1 |
102 |
10-2 |
104 |
10-6 |
10-2 |
102 |
102 |
|
Kg,m,s |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
g,cm,s |
103 |
102 |
1 |
105 |
101 |
107 |
10-3 |
101 |
102 |
102 |
|
g,cm,us |
103 |
102 |
106 |
10-7 |
10-11 |
10-5 |
10-3 |
10-11 |
10-4 |
10-10 |
|
g,mm,s |
103 |
103 |
1 |
106 |
1 |
109 |
10-6 |
1 |
103 |
103 |
|
Ton,mm,s |
10-3 |
103 |
1 |
1 |
10-6 |
103 |
10-12 |
10-6 |
103 |
103 |
|
Slug,ft,sec |
0.068 |
3.28 |
1 |
0.2246 |
0.020 |
0.736 |
1.93x10-3 |
0.0207 |
3.28 |
3.28 |
|
Kg,mm,s |
1 |
103 |
1 |
103 |
10-3 |
106 |
10-9 |
10-3 |
103 |
103 |
|
g,cm,ms |
103 |
102 |
103 |
10-1 |
10-5 |
101 |
10-3 |
10-5 |
10-1 |
10-4 |
|
Kg,mm,ms |
1 |
103 |
103 |
10-3 |
10-9 |
1 |
10-9 |
10-9 |
1 |
10-3 |