Week - 1 - Consistency of units

Aim: Objective of the challenge is to show the detailed conversion factor for gm/mm/ms from the value of measurements(SI Units) as given in the question.Also to find the conversion factors for all the mentioned unit systems

Before moving on to conversion factors, lets have a look at the types of physical quantitites
1)Fundamental quantitites: The physical qunatities which are independent of other quantitites are called as fundamental quantities. Examples: Length(metre), Mass(kg), Time(second), Temperature(kelvin), Electric Current(ampere), Luminous intensity(candela), Amount of substance(mole)
2)Derived quantities: The physical quantities which are derived from fundamental quantities are called as derived quantities. Examples: Density(kg/m3), Volume(m3), Speed(m/s), Force(N)

Some standard values

1) 1kilogram = 1000 grams
2) 1 second = 10^3 milliseconds = 10^6 microseconds
3) Giga = 10^9
4) 1 metre = 1000 millimetre

Detailed calculation for gm/mm/ms from the given values:

1)Mass of 1kg : 10^3 gm
2)Length of 1m : 10^3 mm
3)Time of 1s : 10^3 ms

4)Force of 1N : The conversion factor is 1. The detailed explanation are as follows
we know that Force(1N) = Mass(kg) x Acceleration(m/s2)
Converting (kgm)/s2 into (g-mm)/ms2, we will get
Force(1N) = (1000gm x 1000mm)/(1000ms)^2
Force(1N) = (10^6 gm-mm)/10^6 ms2
Force(1N) = 1 (gm-mm)/ms2

5)Stress of 1Pa : The conversion factor is 1e-6. The detailed explanation are as follows
we know that 1Pa = 1N/m2
1Pa = 1(kgm/s2)/m2
1Pa = 1kg/ms2
So 1kg/ms2 = 1000gm/(1000mm x (10^6ms2))
1kg/ms2 = 1/10^6gm/(mm-ms2)
1kg/ms2 = 1e-6 gm/(mm-ms2)

6)Energy of 1J : The conversion factor is 1e3. The detailed explanation are as follows
we know that 1J = 1N/m
1J = 1(kgm/s2) x m (1N = 1kgm/s2)
1J = 1((1000gm x 1000mm)/1000000ms2) x 1000mm
1J = 1e3(gm*mm2/ms2)

7)Density of 1kg/m3 = The conversion factor is 1e-6. The detailed explanation are as follows
1 kg/m3 = 1000gm/(1000mm x 1000mm x 1000mm)
1 kg/m3 = 1e-6 gm/mm3

8)Young's Modulus of 210 GPa : The conversion factor is 1e3. The detailed explanation are as follows
210 GPa = (210 x 10^9) kg/ms2
210 GPa = (210 x 10^9) x (1000/(10^3 x 10^6))
210 GPa = 210 x 10^3 g/(mm-ms2)

9)Velocity of 56.33 Kmph : The conversion factor is 15.27. The detailed explanation are as follows
We know that 1km = 10^6mm and 1hour = 3600s
56.33 Kmph = 10^6mm/(3600s x 1000m)
56.33 Kmph = 15.27mm/ms
So for 1Kmph = 0.277mm/ms

10)Gravity of 9.8m/s2 : The conversion factor is 1e-3. The detailed explanation are as follows
9.8m/s2 = (9.8 x 1000)/10^6
9.8m/s2 = 9.8e-3
1m/s2 = 1e-3

Conversion factors for other given unit systems

SI UNIT	Mass Kg	Length metre	Time Second	Force 1N	Stress 1Pa	Energy 1J	Density 1 Kg/m3	Young's Modulus 210 GPa	Velocity 56.33Kmph	Gravity
kg/m/s	1 kg	1m	1s	1kgm/s2	1kg/ms2	1kgm2/s2	1kg/m3	210e+9 kg/ms2	15.647 m/s	9.8m/s2
kg/cm/ms	1 kg	10^2 cm	1e+3 ms	1e-4 kg-cm/ms2	1e-8 kg/cm-ms2	1e-2 kg-cm2/ms2	1e-6 kg/cm3	2100 kg/cm-ms2	1.5647 cm/ms	9.8e-4 cm/ms2
kg/cm/s	1 kg	1e+2 cm	1s	1e+2 kg-cm/s2	1e-2 kg/cm-s2	1e+4 kg-cm2/s2	1e-6 kg/cm3	210e+7 kg/cm-s2	1564.7 cm/s	9.8e+2 cm/s2
g/mm/ms	1e+3 gm	1e+3 mm	1e+3 s	1 gm-mm/ms2	1e-6 g/mm-ms2	1e+3 gm-mm2/ms2	1e-6gm/mm3	210e+3 gm/mm-ms2	15.647 mm/ms	9.8e-3 mm/ms2
g/cm/s	1e+3 gm	1e+2 cm	1s	1e+5 gm-cm/s2	10 gm/cm-s2	1e+7 gm-cm2/s2	1e-3 gm/cm3	210e+10 gm/cm-s2	1564.7 cm/s	9.8e+2 cm/s2
g/cm/μs	1e+3 gm	1e+2 cm	1e+6 μs	1e+7 gm-cm/μs2	1e-11 gm/cm-μs2	1e-5 gm-cm2/μs2	1e-3 gm/cm3	2.10 gm/cm-μs2	15.647e-4 cm/μs	9.8e-10 cm/μs2
g/mm/s	1e+3 gm	1e+3 mm	1s	1e+6 gm-mm/s2	1 gm/mm-s2	1e+9 gm-mm2/s2	1e-6 gm/mm3	2.10e+11 gm/mm-s2	15647 mm/s	9.8e+3 mm/s2
ton/mm/s	1e-3 ton	1e+3 mm	1s	1 ton-mm/s2	1e-6 ton/mm-s2	1e+3 ton-mm2/s2	1e-12 ton/mm3	210e+3 ton/mm-s2	15647 mm/s	9.8e+3 mm/s2
slug/ft/s	0.068 slug	3.28 ft	1s	0.2246 slug-ft/s2	0.0208 slug/ft-s2	0.7366 slug-ft2/s2	1.93e-3 slug/ft3	4.368e+9 slug/ft-s2	51.322 ft/s	32.144 ft/s2
kg/mm/s	1 kg	1e+3 mm	1s	1e+3 kg-mm/s2	1e-3 kg/mm-s2	1e+6 kg-mm2/s2	1e-9 kg/mm3	210e+6 kg/mm-s2	15647 mm/s	9.8e+3 mm/s2
g/cm/ms	1e+3 gm	1e+2 cm	1e+3 ms	1e-1 gm-cm/ms2	1e-5 gm/cm-ms2	10 gm-cm2/ms2	1e-3 gm/cm3	210e+4 gm/cm-ms2	1.5647 cm/ms	9.8e-4 cm/ms2
kg/mm/ms	1kg	1e+3 mm	1e+3 ms	1e-3 kg-mm/ms2	1e-9 kg/mm-ms2	1 kg-mm2/ms2	1e-9 kg/mm3	210 kg/mm-ms2	15.647 mm/ms	9.8e-3 mm/ms2