Week - 1 - Consistency of Units

Units/ Quantity mass length time force stress Energy Density Young's modulus Velocity Gravity 1kg 1m 1s 1N 1Pa 1Nm 1 Kg/m3 20 Gpa 56.33 Kmph 9.8 m/s2 kg, cm, ms 1 kg 100 cm 1000 ms 10E-4 kg cm/ms2 10E-8 kg/cm ms2 10E-2 kg cm2/ms2 10E-6 Kg/ cm3 200 kg/cm ms2 1.56 cm/ms 9.810E-4 cm/ms2 gm, mm, ms 1000 g 1000 mm 1000 ms 1 gm mm/ms2 10E-6 gm/mm ms2 1000 gm mm2/ms2 10E-6 g/ mm3 20E3 gm/mm ms2 15.6 mm/ms 9.810E-3 mm/ms2 kg, m, s 1 kg 1 m 1 s 1 N 1 Pa 1Nm 1 Kg/m3 20 GPa 1564.7 m/s2 9.8 m/s2 g, cm, s 1000 g 100 cm 1 s 10E5 gm cm/s2 10 gm/cm s2 10E7 gm cm2/s2 10E-3 g/cm3 20E9 gm/cm s2 156 cm/s 980 cm/s2 g, cm, ms 1000 g 100 cm 1000 ms 0.1 g cm/ms2 10E-5 g/cm ms2 10 g cm2/ms2 10E-3 g/cm3 20E4 g/cm ms2 1.56 cm/ms 9.8E-2 cm/ms2 g, mm, s 1000 g 1000 mm 1 s 10E6 g mm/s2 1 g/mm s2 10E9 g mm2/s2 10E-6g/mm3 2E9 g/mm s2 1560 mm/s 9800 mm/ s2 ton, mm, s 0.001 ton 1000 mm 1 s 1 ton mm/s2 10E-5 ton/mm s2 1000 ton mm2/s2 10E-12 t/ mm3 20E4 ton/mm s2 1560 mm/s 9800 mm/ s2 slug, ft, s 0.0685 slug 3.28 ft 1 s 0.224 slug ft/s2 0.0208 slug/ ft s2 0.7347 slug ft2/s2 1.94E-3 slug/ ft3 4.16E10 slug/ft s2 5132.28 ft/s 32.14 ft/s2 kg, mm, s 1 kg 1000 mm 1 s 1000 kg mm/s2 10E-3 kg/mm s2 10E6 kg mm2/s2 10E-9 kg/ mm3 20E6 kg/mm s2 1560 mm/s 9800 mm/ s2 g, cm, ms 1000 g 100 cm 1000 ms 100 g cm/ms2 10E-2 g/cm ms2 10E4 g cm2/ms2 10E-1 g/ cm3 20E7 g/cm ms2 1.56 cm/ms 9.81E-4 cm/ms2 kg, mm, ms 1 kg 1000 mm 1000 ms 0.001 kg mm/ms2 10E-9 kg/mm ms2 1 kg mm2/ms2 10E-9 kg/mm3 20 kg/mm ms2 15.6 mm/ms 9.81E-3 mm/ms2

Detail conversion of si unit to gm, mm, ms:

The fundamental unit is as it is as given in the table. Only derived units are converted here,

Force:

1N = 1 kg m/s2 = 1* 1000 g * 1000 mm / 10E6 ms2 = 1 g mm/ms2

Stress:

1 Pa = 1 N/m2 = (1 g mm/ms2)/ 10E6 mm2 = 10E-6 g/ mm ms2

Energy:

1Nm = (1 g mm/ms2)* 1000 mm = 1000 g mm2/ ms2

Density:

1 kg/m3 = 1000 g/ 10E9 mm3 = 10E-6 g/mm3

Young's modulus:

1 GPa = 1* 10E9 * N/m2 = 10E9 * 10E-6 g mm/ ms2 = 1000 g mm/ms2

Velocity:

1 m/s2= 1000mm / 10E6 ms2 = 10E-3 mm/ms2

Gravity:

1 m/s2 = 1000 mm/ 10E-6 ms2 =10E9 mm/ms2