Week - 1 - Consistency of Units

Aim:To Convert & Understand the Conversion of given SI Units in required unit System in detail

Given Values Are:

1. MASS 1kg
2. LENGTH 1m
3. TIME 1s
4. FORCE 1N
5. STRESS 1Pa
6. ENERGY 1Nm
7. DENSITY 1Kg/m3
8. YOUNG'S Modulus 210GPa
9. Velocity 56.33KMPH
10. GRAVITY 9.8m/s2

Now We need to convert given SI unit to gm/mm/ms unit system:

1. MASS 1kilogram

• Mass of 1kg(kilogram)=1000gm(gram)=1e+03gm
• So, the conversion factor will be 1e+03

2.LENGTH 1meter

• Length of 1m(meter)=1000mm(milli meter)=1e+03mm
• So, the conversion factor will be 1e+03

3.Time 1second

• Time of 1s(second)=1000ms(milli second)=1e+03ms
• So, the conversion factor will be 1e+03

4.FORCE 1N(Newton)

• Force of 1N(Newton)=1kg.m/s2=1e+03gm.1e+03mm/(1e+03ms)2
• =1e+06gm.mm/1e+06ms2
• here 1e+06 value from numerator and denominator gets cancelled
• Force of 1N=1gm.mm/ms2
• So, the conversion factor will be 1

5.STRESS 1Pa(Pascal)

• 1pa=1N/m2=1gm.mm/ms2.(1e+03mm)2=1gm.mm/ms2.1e+06mm2=1gm/1e+06mm.ms2
• here i have taken N value from Force,
• and converted m2=(1e+03mm)2
• so, by arranging values we get
• 1Pa=1e-06gm/mm.ms2
• So, the conversion factor will be 1e-06

6.ENERGY 1Nm

• Energy of 1Nm=1gm.mm.(1e+03mm)/ms2
• here i have taken N value from Force
• and converted m2=1e+03mm
• so, by arranging values we get
• 1Nm=1e+03gm.mm2/ms2
• So, the conversion factor will be 1e+03

7.DENSITY 1Kg/m3

• Density of 1kg/m3=1e+03gm/(1e+03mm)3=1e+03gm/1e+09mm3
• here i have converted kg to gm shown in mass
• & converted m to mm shown in length
• so, by arranging values we get
• 1kg/m3=1e-06gm/mm3
• So, the conversion factor will be 1e-06

8.YOUNG'S Modulus 210GPa

• YOUNG'S Modulus of 210GPa=210*1e+09*1e-06gm/ms2.mm

• here i have taken G(Giga) Value from engineering standard as 1e+09
• & taken value of Pa(pascal) from stress
• so, by arranging and calculating values we get
• 210GPa=210e+03gm/ms2.mm
• So, the conversion factor will be 1e+03

9.Velocity 56.33KMPH

• Velocity of 56.33KMPH=56.33e+06mm/3.61e+06ms
• Here i have converted value of KM to MM as 1KM=1e+06MM
• & converted value of hour to MilliSec as 1Hour=3.61e+06ms
• so, by arranging and calculating values we get
• Velocity 56.33KMPH=15.61mm/ms
• So, the conversion factor will be 15.61

10.GRAVITY 9.81m/s2

• GRAVITY of 9.81m/s2=9.81e+03mm/(1e+03ms)2=9.81e+03mm/1e+06ms2
• Here i have converted m to mm as 1m=1e+03mm
• & converted s to ms as 1s=1e+03ms
• so, by arranging and calculating values we get
• GRAVITY of 9.8m/s2=9.81e-03mm/ms2
• So, the conversion factor will be 1e-03

Sl.No	Units	Mass(1kg)	Length(1m)	Time(1s)	Force(1N)	Stress(1Pa)	Energy(1Nm)	Density(1kg/m3)	Young's Modulus(210GPa)	Velocity(56.3KMPH)	Gravity(9.81m/s2)
1	Kg cm ms	1 kg	1e+02 cm	1e+03 ms	1e-04 kg.cm/ms2	1 kg/cm.ms2	1e-02 kg.cm2/ms2	1e-06 kg/m3	210e+09 kg/cm.ms2	1.57 cm/ms	9.81e-04 cm/ms2
2	Kg cm s	1 kg	1e+02 cm	1 s	1e+02 kg.cm/s2	1e-02 kg/cm.s2	1e+04 kg.cm2/s2	1e-06 kg/cm3	210e+07 kg/cm.s2	1.5647e+03 cm/s	9.81e+02 cm/s2
3	gm mm ms	1e+03 gm	1e+03 mm	1e+03 ms	1 gm.mm/ms2	1e-06 gm/mm.ms2	1e+03 gm.mm2/ms2	1e-06 gm/mm3	2.10e+05 gm/mm.ms2	15.61 mm/ms	9.81e-03 mm/ms2
4	kg m s	1 kg	1 m	1 s	1 kg.m/s2	1 kg/m.s2	1 kg.m2/s2	1 kg/m3	210e+09 kg/m.s2	15.65 m/s	9.8 m/s2
5	g cm s	1e+03 gm	1e+02 cm	1 s	1e+05 gm.cm/s2	1e+01 gm/cm.s2	1e+03 gm/s2	1e-03 gm/cm3	210e+10 gm/cm.s2	1.56e+03 cm/s	9.81e+02 cm/s2
6	g cm µs	1e+03 gm	1e+02 cm	1e+06 µs(Micro Second)	1e-07 gm.cm/µs2	1e-11 gm/cm.µs2	1e-05 gm.cm2/µs2	1e-03 gm/cm3	210e-02 gm/cm.µs2	1.56e-03 cm/µs	9.81e-10 cm/µs2
7	g mm s	1e+03 gm	1e+03 mm	1 s	1e+06 gm.mm/s2	1e+03 gm/mm.s2	1e+03 gm/s2	1e-06 gm/mm3	210e+12 gm/mm.s2	1.5647e+04 mm/s	9.81e+03 mm/s2
8	ton mm s	1e-03 ton	1e+03 mm	1 s	1 ton.mm/s2	1e-06 ton/mm.s2	1e+03 ton.mm2/s2	1e-12 ton/mm3	210e+03 ton/mm.s2	1.5647e+04 mm/s	9.81e+03 mm/s2
9	slug ft s	6.85e-02 slug	3.281 ft	1 s	2.25e-01 slug.ft/s2	2.087e-02 slug/ft.s2	7.374e-01 slug.ft2/s2	1.94e-03 slug/ft3	4.383e+9 slug/ft.s2	51.33 ft/s	32.19 ft/s2
10	kg mm s	1 kg	1e+03 mm	1 s	1e+03 kg.mm/s2	1e-03 kg/mm.s2	1e+06 kg.mm2/s2	1e-09 kg/mm3	210e+06 kg/mm.s2	1.5647e+04 mm/s	9.81e+03 mm/s2
11	g cm ms	1e+03 gm	1e+02 cm	1e+03 ms	1e-01 gm.cm/ms2	1e-05 gm/cm.ms2	1e+02 gm.cm2/ms2	1e-03 gm/cm3	210e+04 gm/cm.ms2	1.5647 cm/ms	9.81e-04 cm/ms2
12	kg mm ms	1 kg	1e+03 mm	1e+03 ms	1e-03 kg.mm/ms2	1e-09 kg/mm.ms2	1e-06 kg/ms2	1e-09 kg/mm3	210 kg/mm.ms2	15.64 mm/ms	9.81e-03 mm/ms2