Week - 1 - Consistency of Units
Conversion of Units from SI to (gm,mm,ms)
(KG,M,S) (gm,mm,ms)
Mass 1kg 1000g
Length 1m 1000mm
Time 1s 1000ms
Force 1N => mass * acceleration
= kg * m/s^2
= (1000) * 1000/(1000)^2
= 10^6 * 10^-6 (g*mm)/ms^2
= 1(g*mm)/(ms)^2
Stress 1Pa => Pa = N/m^2 => (kg*m/s^2)/m^2
= Kg/(m*s^2)
Kg/(m*s^2) = 1000g/(1000mm*(1000ms)^2)
= 10^-6 g/(mm*ms^2)
Energy 1Nm => 1J = 1Nm = (kg * m/s^2) * m
= (kg * m^2 / s^2)
(kg * m^2 / s^2) = 1000g * (1000mm)^2 / (1000ms)^2
= (10^9 g*mm^2) / (10^6 ms^2)
= 10^3 (g * mm^2/ ms^2)
Density 1kg/m^3 => 1000g/1000mm^3
= 10^-6 g/mm^3
Young's Modulus => 210GPa = 210e+9 kg/ms^2
we know that, 1kg/ms^2 = 10^-6 g/(mm*ms^2)
Therefore, 210e+9 kg(ms^2) = 210e+9*10^-6 g/(mm*ms^2)
= 210e+3g/(mm*m*s^2)
= 210*10^3 g/(mm*m*s^2)
Velocity 56.33kmph = 56.33[10^6 mm/(3600*1000ms)]
= 15.647 mm/ms
Gravity 9.8m/s^2 = 9.8*1000mm/(1000ms)^2
= 9.8*10^-3 mm/ms^2
System of units:
Units Mass length Time Force Stress Energy Density Young's Velocity Gravity
System modulus
Kg cm ms 1kg 10^2cm 10^3ms 10^-4 10^-8 10^-2 10^-6 2100 1.5647 9.8*10^-4
kg*cm/ms2 kg/(cm*ms2) kg*cm2/ms2 kg/cm3 kg/(cm*ms2) cm/ms cm/ms2
Kg cm s 1kg 10^2cm 1s 10^2 10^-2 10^4 10^-6 210e7 1564.7 9.8*10^2
kg*cm/s2 kg/(cm*s2) kg*cm2/s2 kg/cm3 kg/(cm*s2) cm/s cm/s^2
gm mm ms 10^3g 10^3mm 10^3ms 1 10^-6 10^3 10^-6 210e3 15.647 9.8*10^-3
g*mm/ms2 g/(mm*ms2) g*mm2/ms2 g/mm3 g/(mm*ms2) mm/ms mm/ms^2
kg m s 1kg 1m 1s 1N=1 1Pa=1 1J=1Nm 1kg/m3 210GPa 15.647 9.8
kg*m/s2 kg/(m*s2) =1kg*m2/s2 210e9kg/m*s2 m/s m/s2
g cm s 10^3g 10^2cm 1s 10^5 10 10^7 10^-3 210e10 1564.7 9.8*10^2
g*cm/s2 g/(cm*s2) g*cm2/s2 g/cm3 g/(cm*s2) cm/s cm/s2
g cm us 10^3g 10^2cm 10^6us 10^-7 10^-11 10^-5 10^-3 2.10 15.647*10^-4 9.8*10^-10
g*cm/us2 g/(cm*us2) g*cm2/us2 g/cm3 g/(cm*us2) cm/us cm/us2
g mm s 10^3g 10^3mm 1s 10^6 1 10^9 10^-6 2.10e11 15647 9.8*10^3
g*mm/s2 g/(mm*s2) g*mm2/s2 g/mm3 g/(mm*s2) mm/s mm/s2
ton mm s 10^-3ton 10^3mm 1s 1 10^-6 10^3 10^-12 210e3 15647 9.8*10^3
ton*mm/s2 ton/(mm*s2) ton*mm2/s2 ton/mm3 ton/(mm*s2) mm/s mm/s2
slug ft s 0.068slug 3.28ft 1s 0.2246 0.0208 0.7366 1.93*10^-3 4.368e9 51.322 32.144
slug*ft/s2 slug/(ft*s2) slug*ft2/s2 slug/ft3 slug/(ft*s2) ft/s ft/s2
kg mm s 1kg 10^3mm 1s 10^3 10^-3 10^6 10^-9 210e6 15647 9.8*10^3
kg*mm/s2 kg/(mm*s2) kg*mm2/s2 kg/mm3 kg/(mm*s2) mm/s mm/s2
g cm ms 10^3g 10^2cm 10^3ms 10^-1 10^-5 10 10^-3 210e4 1.5647 9.8*10^-4
g*cm/ms2 g/(cm*ms2) g*cm2/ms2 g/cm3 g/(cm*ms2) cm/ms cm/ms2
kg mm ms 1kg 10^3mm 10^3ms 10^-3 10^-9 1 10^-9 210 15.647 9.8*10^-3
kg*mm/ms2 kg/(mm*ms2) kg*mm2/ms2 kg/mm3 kg/(mm*ms2) mm/ms mm/ms2
Conversion Factors:
Kg, m, s
Force: Conversion factor=1
Stress: Conversion factor=1
Energy: Conversion factor=1
Density: Conversion factor=1
Young's Modulus: Conversion factor=10^9
Velocity: Conversion factor=1
Gravity: Conversion factor=1
Kg, cm, ms
Force: Conversion factor=10^-4
Stress: Conversion factor=10^-8
Energy: Conversion factor=10^-2
Density: Conversion factor=10^-6
Young's Modulus: Conversion factor=10
Velocity: Conversion factor=1
Gravity: Conversion factor=10^-4
Kg, cm, s
Force: Conversion factor=10^2
Stress: Conversion factor=10^-2
Energy: Conversion factor=10^4
Density: Conversion factor=10^-6
Young's Modulus: Conversion factor=10^7
Velocity: Conversion factor=1
Gravity: Conversion factor=10^2
g, cm, s
Force: Conversion factor=10^5
Stress: Conversion factor=10
Energy: Conversion factor=10^7
Density: Conversion factor=10^-3
Young's Modulus: Conversion factor=10^10
Velocity: Conversion factor=1
Gravity: Conversion factor=10^2
g,cm,us
Force: Conversion factor=10^-7
Stress: Conversion factor=10^-11
Energy: Conversion factor10^-5
Density: Conversion factor=10^-3
Young's Modulus: Conversion factor=10^-2
Velocity: Conversion factor=10^-4
Gravity: Conversion factor=10^-10
g, mm, s
Force: Conversion factor=10^6
Stress: Conversion factor=1
Energy: Conversion factor=10^9
Density: Conversion factor=10^-6
Young's Modulus: Conversion factor=10^9
Velocity: Conversion factor=1
Gravity: Conversion factor=10^3
ton, mm, s
Force: Conversion factor=1
Stress: Conversion factor=10^-6
Energy: Conversion factor=10^3
Density: Conversion factor=10^-12
Young's Modulus: Conversion factor=10^3
Velocity: Conversion factor=1
Gravity: Conversion factor=10^3
slug, ft, s
Force: Conversion factor=1
Stress: Conversion factor=1
Energy: Conversion factor=1
Density: Conversion factor=10^-3
Young's Modulus: Conversion factor=10^9
Velocity: Conversion factor=1
Gravity: Conversion factor=1
Kg, mm, s
Force: Conversion factor=10^3
Stress: Conversion factor=10^-3
Energy: Conversion factor=10^6
Density: Conversion factor=10^-9
Young's Modulus: Conversion factor=10^6
Velocity: Conversion factor=1
Gravity: Conversion factor=10^3
g, cm, ms
Force: Conversion factor=10^-1
Stress: Conversion factor=10^-5
Energy: Conversion factor=10
Density: Conversion factor=10^-3
Young's Modulus: Conversion factor=10^4
Velocity: Conversion factor=1
Gravity: Conversion factor=10^-4
Kg, mm, ms
Force: Conversion factor=10^-3
Stress: Conversion factor=10^-9
Energy: Conversion factor=1
Density: Conversion factor=10^-9
Young's Modulus: Conversion factor=1
Velocity: Conversion factor=1
Gravity: Conversion factor=10^3