Week - 1 - Consistency of units
All parameters are converted to their respective unit system with SI Unit system as standard. (kg,m,s)
Calculation of the conversion from SI unit to g,mm,ms
|
SI Unit system (kg, m, s) |
Conversion to (g, mm, ms) |
|
MASS 1kg |
1000g (grams) |
|
LENGTH 1m |
1000mm (milli meter) |
|
TIME 1s |
1000ms (milli seconds) |
|
FORCE 1N |
1N = 1mass*1acceleration = 1kg*1 m/s2 = (1000g*1000mm)/(1000ms)2 = 106*10-6 (g*mm)/ms2 = 1 (g*mm)/ms2 Conversion factor = 1 |
|
STRESS 1Pa |
1 Pa = 1N/m2 = {1kg*(1 m/s2)}/m2 = 1 kg/ (m* s2) So, 1 kg/ (m* s2) = 1000g/{1000mm*(1000ms)2} = 10-6 g/ (mm*ms2) Conversion factor = 10-6 |
|
ENERGY 1Nm |
1 J = 1Nm = (1kg*1 m/s2) * m = 1 (kg*m2/s2) Now, 1 (kg*m2/s2) = {1000g * (1000mm)2}/(1000ms)2 = (109 g*mm2) / (106 ms2) = 103 (g*mm2/ ms2) Conversion factor = 103 |
|
DENSITY 1Kg/m3 |
1Kg/m3 = 1000g/(1000mm)3 = 10-6 g/mm3 Conversion factor = 10-6 |
|
YOUNG'S Modulus 210GPa |
210 GPa = 210e+9 kg/(m*s2) Here we already have 1 kg/ (m* s2) while calculating the stress 1 kg/ (m* s2) = 1000g/{1000mm*(1000ms)2} = 10-6 g/(mm*m s2) Therefore, 210e+9 kg/(m*s2) = 210e+9 * 10-6 g/ (mm*m s2) = 210e+3 g/ (mm*m s2) = 210*103 g/ (mm*m s2) Conversion factor = 103 |
|
Velocity 56.33Kmph |
56.33 Kmph = 56.33 * {106mm/(3600*1000ms)} = 15.647 mm/ms Conversion factor =5/18 |
|
GRAVITY 9.8m/s2 |
9.8m/s2 = 9.8 * 1000mm/(1000ms)2 = 9.8* 10-3 mm/ms2 Conversion factor = 10-3 |
System of Units Table:
|
Unit system |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
SI Unit kg m s |
1kg |
1m |
1s |
1 N =1 kg*m/s2 |
1 Pa = 1 kg/(m* s2) |
1 J = 1Nm = 1 kg*m2/s2 |
1kg/m3 |
210 GPa = 210e+9 kg/(m*s2) |
15.647 m/s |
9.8 m/s2 |
|
kg cm ms |
1kg |
102cm |
103ms |
10-4 kg*cm/ms2 |
10-8 kg/(cm*ms2) |
10-2 kg*cm2/ms2 |
10-6 kg/cm3 |
2100 kg/(cm*ms2) |
1.5647 cm/ms |
9.8*10-4 cm/ms2 |
|
kg cm s |
1kg |
102cm |
1s |
102 kg*cm/s2 |
10-2 kg/(cm*s2) |
104 kg*cm2/s2 |
10-6 kg/cm3 |
210e+7 kg/(cm*s2) |
1564.7 cm/s |
9.8*102 cm/s2 |
|
g mm ms |
103g |
103mm |
103ms |
1 g*mm/ms2 |
10-6 g/(mm*ms2) |
103 g*mm2/ms2 |
10-6 g/mm3 |
210e+3 g/(mm*ms2) |
15.647 mm/ms |
9.8*10-3 mm/ms2 |
|
g cm s |
103g |
102cm |
1s |
105 g*cm/s2 |
10 g/(cm*s2) |
107 g*cm2/s2 |
10-3 g/cm3 |
210e+10 g/(cm*s2) |
1564.7 cm/s |
9.8*102 cm/s2 |
|
g cm μs |
103g |
102cm |
106μs |
10-7 g*cm/μs2 |
10-11 g/(cm*μs2) |
10-5 g*cm2/μs2 |
10-3 g/cm3 |
2.10 g/(cm*μs2) |
15.647*10-4 cm/ μs |
9.8*10-10 cm/μs2 |
|
g mm s |
103g |
103mm |
1s |
106 g*mm/ s2 |
1 g/(mm*s2) |
109 g*mm2/s2 |
10-6 g/mm3 |
2.10 e+11 g/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
Ton mm s |
10-3ton |
103mm |
1s |
1 ton*mm/s2 |
10-6 ton/(mm*s2) |
103 ton*mm2/s2 |
10-12 ton/mm3 |
210e+3 ton/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
slug ft s |
0.068slug |
3.28 ft |
1s |
0.2246 slug*ft/ s2 |
0.0208 slug/(ft*s2) |
0.7366 slug*ft2/s2 |
1.93*10-3 slug/ft3 |
4.368 e+9 slug/(ft*s2) |
51.322 ft/s |
32.144 ft/s2 |
|
kg mm s |
1kg |
103mm |
1s |
103 kg*mm/s2 |
10-3 kg/(mm*s2) |
106 kg*mm2/s2 |
10-9 kg/mm3 |
210e+6 kg/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
g cm ms |
103g |
102cm |
103ms |
10-1 g*cm/ms2 |
10-5 g/(cm*ms2) |
10 g*cm2/ms2 |
10-3 g/cm3 |
210e+4 g/(cm*ms2) |
1.5647 cm/ms |
9.8*10-4 cm/ ms2 |
|
kg mm ms |
1kg |
103mm |
103ms |
10-3 kg*mm/ms2 |
10-9 kg/(mm*ms2) |
1 kg*mm2/ms2 |
10-9 kg/mm3 |
210 kg/(mm*ms2) |
15.647 mm/ms |
9.8*10-3 mm/ms2 |
The Conversion factor for parameters in other unit system are as follows:
Unit system:
kg m s
Force : 1 kg*m/s2 conversion factor = 1
Stress : 1 kg/(m*s2) conversion factor = 1
Energy: 1 kg*m2/s2 conversion factor = 1
Density: 1 kg/m3 conversion factor = 1
Young's Modulus: 210 e+9 kg/(m*s2) conversion factor = 109
Velocity: 15.647 m/s conversion factor = 1
Gravity: 9.8 m/s2 conversion factor = 1
kg cm ms
Force : 10-4 kg*cm/ms2 conversion factor = 10-4
Stress : 10-8 kg/(cm*ms2) conversion factor = 10-8
Energy: 10-2 kg*cm2/ms2 conversion factor = 10-2
Density: 10-6 kg/cm3 conversion factor = 10-6
Young's Modulus: 2100 kg/(cm*ms2) conversion factor = 10
Velocity: 1.5647 cm/ms conversion factor = 1
Gravity: 9.8*10-4 cm/ms2 conversion factor = 10-4
kg cm s
Force : 102 kg*cm/s2 conversion factor = 102
Stress : 10-2 kg/(cm*s2) conversion factor = 10-2
Energy: 104 kg*cm2/s2 conversion factor = 104
Density: 10-6 kg/cm3 conversion factor = 10-6
Young's Modulus: 210e+7 kg/(cm*s2) conversion factor = 107
Velocity: 1564.7 cm/s conversion factor = 1
Gravity: 9.8*102 cm/s2 conversion factor = 102
g cm s
Force : 105 g*cm/s2 conversion factor = 105
Stress : 10 g/(cm*s2) conversion factor = 10
Energy: 107 g*cm2/s2 conversion factor = 107
Density: 10-3 g/cm3 conversion factor = 10-3
Young's Modulus: 210e+10 g/(cm*s2) conversion factor = 1010
Velocity: 1564.7 cm/s conversion factor = 1
Gravity: 9.8*102 cm/s2 conversion factor = 102
g cm μs
Force : 10-7 g*cm/μs2 conversion factor = 10-7
Stress : 10-11 g/(cm*μs2) conversion factor = 10-11
Energy: 10-5 g*cm2/μs2 conversion factor = 10-5
Density: 10-3 g/cm3 conversion factor = 10-3
Young's Modulus: 2.10 g/(cm*μs2) conversion factor = 10-2
Velocity:15.647*10-4 cm/μs conversion factor = 10-4
Gravity:9.8*10-10 cm/μs2 conversion factor = 10-10
g mm s
Force : 106 g*mm/s2 conversion factor = 106
Stress :1 g/(mm*s2) conversion factor = 1
Energy: 109 g*mm2/s2 conversion factor = 109
Density: 10-6 g/mm3 conversion factor = 10-6
Young's Modulus: 210 e+9 g/(mm*s2) conversion factor = 109
Velocity:15647 mm/s conversion factor = 1
Gravity:9.8*103 mm/s2 conversion factor = 103
ton mm s
Force :1 ton*mm/s2 conversion factor = 1
Stress :10-6 ton/(mm*s2) conversion factor = 10-6
Energy: 103 ton*mm2/s2 conversion factor = 103
Density: 10-12 ton/mm3 conversion factor = 10-12
Young's Modulus: 210 e+3 ton/(mm*s2) conversion factor = 103
Velocity: 15647 mm/s conversion factor = 1
Gravity: 9.8*103 mm/s2 conversion factor = 103
slug ft s
Force : 0.2246 slug*ft/s2 conversion factor = 1
Stress : 0.0208 slug/(ft*s2) conversion factor = 1
Energy: 0.7366 slug*ft2/s2 conversion factor = 1
Density: 1.93*10-3 slug/ft3 conversion factor = 10-3
Young's Modulus: 4.368 e+9 slug/(ft*s2) conversion factor = 109
Velocity: 51.322 ft/s conversion factor = 1
Gravity: 32.144 ft/s2 conversion factor = 1
kg mm s
Force : 103 kg*mm/s2 conversion factor = 103
Stress :10-3 kg/(mm*s2) conversion factor = 10-3
Energy: 106 kg*mm2/s2 conversion factor = 106
Density: 10-9 kg/mm3 conversion factor = 10-9
Young's Modulus: 210 e+6 kg/(mm*s2) conversion factor = 106
Velocity:15647 mm/s conversion factor = 1
Gravity: 9.8*103 mm/s2 conversion factor = 103
g cm ms
Force : 10-1 g*cm/ms2 conversion factor = 10-1
Stress : 10-5 g/(cm*ms2) conversion factor = 10-5
Energy: 10 g*cm2/ms2 conversion factor = 10
Density: 10-3 g/cm3 conversion factor = 10-3
Young's Modulus: 210 e+4 g/(cm*ms2) conversion factor = 104
Velocity:1.5647 cm/ms conversion factor = 1
Gravity: 9.8*10-4 cm/ms2 conversion factor = 10-4
kg mm ms
Force : 10-3 kg*mm/ms2 conversion factor = 10-3
Stress : 10-9 kg/(mm*ms2) conversion factor = 10-9
Energy: 1 kg*mm2/ms2 conversion factor = 1
Density: 10-9 kg/mm3 conversion factor = 10-9
Young's Modulus: 210 kg/(mm*ms2) conversion factor = 1
Velocity: 15.647 mm/ms conversion factor = 1
Gravity: 9.8*103 mm/ms2 conversion factor = 103